diff --git a/src/wp-includes/rest-api/endpoints/class-wp-rest-comments-controller.php b/src/wp-includes/rest-api/endpoints/class-wp-rest-comments-controller.php
index 1fa960d58488c..277e2305bc5b0 100644
--- a/src/wp-includes/rest-api/endpoints/class-wp-rest-comments-controller.php
+++ b/src/wp-includes/rest-api/endpoints/class-wp-rest-comments-controller.php
@@ -326,10 +326,9 @@ public function get_items( $request ) {
 
 		$query        = new WP_Comment_Query();
 		$query_result = $query->query( $prepared_args );
+		$comments     = array();
 
 		if ( ! $is_head_request ) {
-			$comments = array();
-
 			foreach ( $query_result as $comment ) {
 				if ( ! $this->check_read_permission( $comment, $request ) ) {
 					continue;
@@ -1243,7 +1242,18 @@ public function prepare_item_for_response( $item, $request ) {
 		$response = rest_ensure_response( $data );
 
 		if ( rest_is_field_included( '_links', $fields ) || rest_is_field_included( '_embedded', $fields ) ) {
-			$response->add_links( $this->prepare_links( $comment ) );
+			$links = $this->prepare_links( $comment );
+			$response->add_links( $links );
+
+			if ( ! empty( $links['self']['href'] ) ) {
+				$actions = $this->get_available_actions( $comment, $request );
+
+				$self = $links['self']['href'];
+
+				foreach ( $actions as $rel ) {
+					$response->add_link( $rel, $self );
+				}
+			}
 		}
 
 		/**
@@ -1346,6 +1356,32 @@ protected function prepare_links( $comment ) {
 		return $links;
 	}
 
+	/**
+	 * Gets the link relations available for the comment and current user.
+	 *
+	 * @since 7.2.0
+	 *
+	 * @param WP_Comment      $comment Comment object.
+	 * @param WP_REST_Request $request Request object.
+	 * @return string[] List of link relations.
+	 */
+	protected function get_available_actions( $comment, $request ) {
+		if ( 'edit' !== $request['context'] ) {
+			return array();
+		}
+
+		$rels = array();
+
+		if ( 'trash' !== $comment->comment_approved && $this->check_edit_permission( $comment ) ) {
+			/** This filter is documented in wp-includes/rest-api/endpoints/class-wp-rest-comments-controller.php */
+			if ( apply_filters( 'rest_comment_trashable', ( EMPTY_TRASH_DAYS > 0 ), $comment ) ) {
+				$rels[] = 'https://api.w.org/action-trash';
+			}
+		}
+
+		return $rels;
+	}
+
 	/**
 	 * Prepends internal property prefix to query parameters to match our response fields.
 	 *
diff --git a/src/wp-includes/rest-api/endpoints/class-wp-rest-menu-items-controller.php b/src/wp-includes/rest-api/endpoints/class-wp-rest-menu-items-controller.php
index 919714c5a96ef..25ff7be699759 100644
--- a/src/wp-includes/rest-api/endpoints/class-wp-rest-menu-items-controller.php
+++ b/src/wp-includes/rest-api/endpoints/class-wp-rest-menu-items-controller.php
@@ -691,6 +691,23 @@ protected function prepare_links( $post ) {
 		return $links;
 	}
 
+	/**
+	 * Gets the link relations available for the menu item and current user.
+	 *
+	 * Menu items can only be deleted permanently, so the `action-trash` link is skipped.
+	 *
+	 * @since 7.2.0
+	 *
+	 * @param WP_Post         $post    Post object.
+	 * @param WP_REST_Request $request Request object.
+	 * @return array List of link relations.
+	 */
+	protected function get_available_actions( $post, $request ) {
+		$rels = parent::get_available_actions( $post, $request );
+
+		return array_values( array_diff( $rels, array( 'https://api.w.org/action-trash' ) ) );
+	}
+
 	/**
 	 * Retrieves Link Description Objects that should be added to the Schema for the nav menu items collection.
 	 *
@@ -700,6 +717,7 @@ protected function prepare_links( $post ) {
 	 */
 	protected function get_schema_links() {
 		$links   = parent::get_schema_links();
+		$links   = array_values( wp_list_filter( $links, array( 'rel' => 'https://api.w.org/action-trash' ), 'NOT' ) );
 		$href    = rest_url( "{$this->namespace}/{$this->rest_base}/{id}" );
 		$links[] = array(
 			'rel'          => 'https://api.w.org/menu-item-object',
diff --git a/src/wp-includes/rest-api/endpoints/class-wp-rest-posts-controller.php b/src/wp-includes/rest-api/endpoints/class-wp-rest-posts-controller.php
index 7310de28065e8..e276afe5a7d3d 100644
--- a/src/wp-includes/rest-api/endpoints/class-wp-rest-posts-controller.php
+++ b/src/wp-includes/rest-api/endpoints/class-wp-rest-posts-controller.php
@@ -455,9 +455,8 @@ static function ( $format ) {
 			add_filter( 'post_password_required', array( $this, 'check_password_required' ), 10, 2 );
 		}
 
+		$posts = array();
 		if ( ! $is_head_request ) {
-			$posts = array();
-
 			update_post_author_caches( $query_result );
 			update_post_parent_caches( $query_result );
 
@@ -2334,6 +2333,7 @@ protected function prepare_links( $post ) {
 	 * Gets the link relations available for the post and current user.
 	 *
 	 * @since 4.9.8
+	 * @since 7.2.0 Added the `action-trash` link relation.
 	 *
 	 * @param WP_Post         $post    Post object.
 	 * @param WP_REST_Request $request Request object.
@@ -2369,6 +2369,19 @@ protected function get_available_actions( $post, $request ) {
 			}
 		}
 
+		if ( 'trash' !== $post->post_status && $this->check_delete_permission( $post ) ) {
+			$supports_trash = ( EMPTY_TRASH_DAYS > 0 );
+
+			if ( 'attachment' === $post->post_type ) {
+				$supports_trash = $supports_trash && MEDIA_TRASH;
+			}
+
+			/** This filter is documented in wp-includes/rest-api/endpoints/class-wp-rest-posts-controller.php */
+			if ( apply_filters( "rest_{$this->post_type}_trashable", $supports_trash, $post ) ) {
+				$rels[] = 'https://api.w.org/action-trash';
+			}
+		}
+
 		$taxonomies = wp_list_filter( get_object_taxonomies( $this->post_type, 'objects' ), array( 'show_in_rest' => true ) );
 
 		foreach ( $taxonomies as $tax ) {
@@ -2840,6 +2853,7 @@ public function get_item_schema() {
 	 * Retrieves Link Description Objects that should be added to the Schema for the posts collection.
 	 *
 	 * @since 4.9.8
+	 * @since 7.2.0 Added the `action-trash` link relation.
 	 *
 	 * @return array
 	 */
@@ -2914,6 +2928,12 @@ protected function get_schema_links() {
 			);
 		}
 
+		$links[] = array(
+			'rel'   => 'https://api.w.org/action-trash',
+			'title' => __( 'The current user can move this post to the trash.' ),
+			'href'  => $href,
+		);
+
 		$taxonomies = wp_list_filter( get_object_taxonomies( $this->post_type, 'objects' ), array( 'show_in_rest' => true ) );
 
 		foreach ( $taxonomies as $tax ) {
diff --git a/tests/phpunit/tests/rest-api/rest-attachments-controller.php b/tests/phpunit/tests/rest-api/rest-attachments-controller.php
index aa6355d64b309..cdcf0fc99cae1 100644
--- a/tests/phpunit/tests/rest-api/rest-attachments-controller.php
+++ b/tests/phpunit/tests/rest-api/rest-attachments-controller.php
@@ -2635,6 +2635,27 @@ public function test_publish_action_link_does_not_exists() {
 		$this->assertArrayNotHasKey( 'https://api.w.org/action-publish', $links );
 	}
 
+	/**
+	 * @ticket 63670
+	 *
+	 * @covers WP_REST_Posts_Controller::get_available_actions
+	 */
+	public function test_trash_action_link_does_not_exist_without_media_trash() {
+		$this->assertFalse( MEDIA_TRASH, 'The test expects the default MEDIA_TRASH value.' );
+
+		wp_set_current_user( self::$editor_id );
+
+		$post = self::factory()->attachment->create( array( 'post_author' => self::$editor_id ) );
+
+		$request = new WP_REST_Request( 'GET', "/wp/v2/media/{$post}" );
+		$request->set_query_params( array( 'context' => 'edit' ) );
+
+		$response = rest_get_server()->dispatch( $request );
+		$links    = $response->get_links();
+
+		$this->assertArrayNotHasKey( 'https://api.w.org/action-trash', $links );
+	}
+
 	protected function check_post_data( $attachment, $data, $context = 'view', $links = array() ) {
 		parent::check_post_data( $attachment, $data, $context, $links );
 
diff --git a/tests/phpunit/tests/rest-api/rest-comments-controller.php b/tests/phpunit/tests/rest-api/rest-comments-controller.php
index 1ef7eab22ae6c..c9e6b56b87335 100644
--- a/tests/phpunit/tests/rest-api/rest-comments-controller.php
+++ b/tests/phpunit/tests/rest-api/rest-comments-controller.php
@@ -3494,15 +3494,19 @@ protected function check_comment_data( $data, $context, $links ) {
 		$this->assertSame( mysql_to_rfc3339( $comment->comment_date_gmt ), $data['date_gmt'] );
 		$this->assertSame( get_comment_link( $comment ), $data['link'] );
 		$this->assertArrayHasKey( 'author_avatar_urls', $data );
-		$this->assertSameSets(
-			array(
-				'self',
-				'collection',
-				'up',
-			),
-			array_keys( $links )
+
+		$expected_links = array(
+			'self',
+			'collection',
+			'up',
 		);
 
+		if ( 'edit' === $context ) {
+			$expected_links[] = 'https://api.w.org/action-trash';
+		}
+
+		$this->assertSameSets( $expected_links, array_keys( $links ) );
+
 		if ( $comment->comment_post_ID ) {
 			$this->assertSame( rest_url( '/wp/v2/posts/' . $comment->comment_post_ID ), $links['up'][0]['href'] );
 		}
@@ -4189,6 +4193,43 @@ public function test_get_note_with_children_link() {
 		$this->assertStringContainsString( 'type=note', $children[0]['href'] );
 	}
 
+	/**
+	 * @ticket 63670
+	 *
+	 * @covers WP_REST_Comments_Controller::get_available_actions
+	 */
+	public function test_trash_action_link_does_not_exist_when_not_trashable() {
+		add_filter( 'rest_comment_trashable', '__return_false' );
+		wp_set_current_user( self::$moderator_id );
+
+		$request = new WP_REST_Request( 'GET', sprintf( '/wp/v2/comments/%d', self::$approved_id ) );
+		$request->set_param( 'context', 'edit' );
+		$response = rest_get_server()->dispatch( $request );
+
+		$this->assertArrayNotHasKey( 'https://api.w.org/action-trash', $response->get_links() );
+	}
+
+	/**
+	 * @ticket 63670
+	 *
+	 * @covers WP_REST_Comments_Controller::get_available_actions
+	 */
+	public function test_trash_action_link_does_not_exist_for_trashed_comment() {
+		$comment_id = self::factory()->comment->create(
+			array(
+				'comment_approved' => 'trash',
+				'comment_post_ID'  => self::$post_id,
+			)
+		);
+		wp_set_current_user( self::$moderator_id );
+
+		$request = new WP_REST_Request( 'GET', sprintf( '/wp/v2/comments/%d', $comment_id ) );
+		$request->set_param( 'context', 'edit' );
+		$response = rest_get_server()->dispatch( $request );
+
+		$this->assertArrayNotHasKey( 'https://api.w.org/action-trash', $response->get_links() );
+	}
+
 	/**
 	 * Test retrieving comments by type as authenticated user.
 	 *
diff --git a/tests/phpunit/tests/rest-api/rest-posts-controller.php b/tests/phpunit/tests/rest-api/rest-posts-controller.php
index 1dd9805c21692..c85e9af679be3 100644
--- a/tests/phpunit/tests/rest-api/rest-posts-controller.php
+++ b/tests/phpunit/tests/rest-api/rest-posts-controller.php
@@ -5229,6 +5229,22 @@ public function test_sticky_action_ldo_not_registered_for_non_posts() {
 		$this->assertCount( 0, $publish, 'LDO found on schema.' );
 	}
 
+	/**
+	 * @ticket 63670
+	 *
+	 * @covers WP_REST_Posts_Controller::get_schema_links
+	 */
+	public function test_trash_action_ldo_registered() {
+		$response = rest_get_server()->dispatch( new WP_REST_Request( 'OPTIONS', '/wp/v2/posts' ) );
+		$data     = $response->get_data();
+		$schema   = $data['schema'];
+
+		$this->assertArrayHasKey( 'links', $schema );
+		$trash = wp_list_filter( $schema['links'], array( 'rel' => 'https://api.w.org/action-trash' ) );
+
+		$this->assertCount( 1, $trash, 'LDO found on schema.' );
+	}
+
 	public function test_author_action_ldo_registered_for_post_types_with_author_support() {
 		$response = rest_get_server()->dispatch( new WP_REST_Request( 'OPTIONS', '/wp/v2/posts' ) );
 		$data     = $response->get_data();
@@ -5373,6 +5389,62 @@ public function test_sticky_action_does_not_exist_for_non_post_posts() {
 		$this->assertArrayNotHasKey( 'https://api.w.org/action-sticky', $links );
 	}
 
+	/**
+	 * @ticket 63670
+	 *
+	 * @covers WP_REST_Posts_Controller::get_available_actions
+	 */
+	public function test_trash_action_exists_for_author() {
+		wp_set_current_user( self::$author_id );
+
+		$post = self::factory()->post->create( array( 'post_author' => self::$author_id ) );
+
+		$request = new WP_REST_Request( 'GET', "/wp/v2/posts/{$post}" );
+		$request->set_query_params( array( 'context' => 'edit' ) );
+
+		$response = rest_get_server()->dispatch( $request );
+		$links    = $response->get_links();
+
+		$this->assertArrayHasKey( 'https://api.w.org/action-trash', $links );
+	}
+
+	/**
+	 * @ticket 63670
+	 *
+	 * @covers WP_REST_Posts_Controller::get_available_actions
+	 */
+	public function test_trash_action_does_not_exist_when_not_trashable() {
+		add_filter( 'rest_post_trashable', '__return_false' );
+		wp_set_current_user( self::$editor_id );
+
+		$request = new WP_REST_Request( 'GET', '/wp/v2/posts/' . self::$post_id );
+		$request->set_query_params( array( 'context' => 'edit' ) );
+
+		$response = rest_get_server()->dispatch( $request );
+		$links    = $response->get_links();
+
+		$this->assertArrayNotHasKey( 'https://api.w.org/action-trash', $links );
+	}
+
+	/**
+	 * @ticket 63670
+	 *
+	 * @covers WP_REST_Posts_Controller::get_available_actions
+	 */
+	public function test_trash_action_does_not_exist_for_trashed_post() {
+		wp_set_current_user( self::$editor_id );
+
+		$post = self::factory()->post->create( array( 'post_status' => 'trash' ) );
+
+		$request = new WP_REST_Request( 'GET', "/wp/v2/posts/{$post}" );
+		$request->set_query_params( array( 'context' => 'edit' ) );
+
+		$response = rest_get_server()->dispatch( $request );
+		$links    = $response->get_links();
+
+		$this->assertArrayNotHasKey( 'https://api.w.org/action-trash', $links );
+	}
+
 
 	public function test_assign_author_action_exists_for_editor() {
 		wp_set_current_user( self::$editor_id );
diff --git a/tests/phpunit/tests/rest-api/wpRestMenuItemsController.php b/tests/phpunit/tests/rest-api/wpRestMenuItemsController.php
index 514fa3835717b..85d5618ab964c 100644
--- a/tests/phpunit/tests/rest-api/wpRestMenuItemsController.php
+++ b/tests/phpunit/tests/rest-api/wpRestMenuItemsController.php
@@ -183,6 +183,38 @@ public function test_get_item() {
 		$this->check_get_menu_item_response( $response, 'view' );
 	}
 
+	/**
+	 * @ticket 63670
+	 *
+	 * @covers ::get_available_actions
+	 */
+	public function test_get_item_has_no_trash_action_link() {
+		wp_set_current_user( self::$admin_id );
+		$request = new WP_REST_Request( 'GET', sprintf( '/wp/v2/menu-items/%d', $this->menu_item_id ) );
+		$request->set_param( 'context', 'edit' );
+		$response = rest_get_server()->dispatch( $request );
+		$links    = $response->get_links();
+
+		$this->assertArrayHasKey( 'self', $links, 'The response should have a self link.' );
+		$this->assertArrayNotHasKey( 'https://api.w.org/action-trash', $links, 'The response should not have a trash action link.' );
+	}
+
+	/**
+	 * @ticket 63670
+	 *
+	 * @covers ::get_schema_links
+	 */
+	public function test_trash_action_ldo_not_registered() {
+		$response = rest_get_server()->dispatch( new WP_REST_Request( 'OPTIONS', '/wp/v2/menu-items' ) );
+		$data     = $response->get_data();
+		$schema   = $data['schema'];
+
+		$this->assertArrayHasKey( 'links', $schema );
+		$trash = wp_list_filter( $schema['links'], array( 'rel' => 'https://api.w.org/action-trash' ) );
+
+		$this->assertCount( 0, $trash, 'LDO found on schema.' );
+	}
+
 	/**
 	 * @ticket 54304
 	 * @covers ::get_items