diff --git a/tests/phpunit/tests/functions/wpScheduleDeleteOldPrivacyExportFiles.php b/tests/phpunit/tests/functions/wpScheduleDeleteOldPrivacyExportFiles.php
new file mode 100644
index 0000000000000..fb64d6f81f190
--- /dev/null
+++ b/tests/phpunit/tests/functions/wpScheduleDeleteOldPrivacyExportFiles.php
@@ -0,0 +1,67 @@
+<?php
+
+/**
+ * Tests for the wp_schedule_delete_old_privacy_export_files() function.
+ *
+ * @group functions
+ *
+ * @covers ::wp_schedule_delete_old_privacy_export_files
+ */
+class Tests_Functions_wpScheduleDeleteOldPrivacyExportFiles extends WP_UnitTestCase {
+
+	/**
+	 * Setup test
+	 */
+	public function set_up() {
+		parent::set_up();
+		wp_clear_scheduled_hook( 'wp_privacy_delete_old_export_files' );
+	}
+
+	public function tear_down() {
+		wp_clear_scheduled_hook( 'wp_privacy_delete_old_export_files' );
+
+		parent::tear_down();
+	}
+
+	/**
+	 * check that a schedule is set
+	 *
+	 * @ticket 59707
+	 */
+	public function test_wp_schedule_delete_old_privacy_export_files() {
+
+		$this->assertFalse( wp_next_scheduled( 'wp_privacy_delete_old_export_files' ), 'no export should be scheduled' );
+		wp_schedule_delete_old_privacy_export_files();
+		$this->assertIsInt( wp_next_scheduled( 'wp_privacy_delete_old_export_files' ), 'export should be scheduled' );
+	}
+
+	/**
+	 * check that no schedule is set when WP is in installing mode
+	 *
+	 * @ticket 59707
+	 */
+	public function test_wp_schedule_delete_old_privacy_export_files_is_installing() {
+		// set to installing mode
+		$prior = wp_installing();
+		wp_installing( true );
+
+		$this->assertFalse( wp_next_scheduled( 'wp_privacy_delete_old_export_files' ), 'no export should be scheduled' );
+		wp_schedule_delete_old_privacy_export_files();
+		$this->assertFalse( wp_next_scheduled( 'wp_privacy_delete_old_export_files' ), 'export should be scheduled' );
+
+		wp_installing( $prior );
+	}
+
+	/**
+	 * Check that calling the function when already scheduled does not create a duplicate.
+	 *
+	 * @ticket 59707
+	 */
+	public function test_wp_schedule_delete_old_privacy_export_files_already_scheduled() {
+		wp_schedule_delete_old_privacy_export_files();
+		$first = wp_next_scheduled( 'wp_privacy_delete_old_export_files' );
+
+		wp_schedule_delete_old_privacy_export_files();
+		$this->assertSame( $first, wp_next_scheduled( 'wp_privacy_delete_old_export_files' ) );
+	}
+}