diff --git a/src/wp-admin/includes/privacy-tools.php b/src/wp-admin/includes/privacy-tools.php
index 4f3379bff8909..8a24dc3d74fbc 100644
--- a/src/wp-admin/includes/privacy-tools.php
+++ b/src/wp-admin/includes/privacy-tools.php
@@ -548,6 +548,9 @@ function wp_privacy_generate_personal_data_export_file( $request_id ) {
 		$zip->close();
 
 		if ( ! $error ) {
+			// Schedule the (one-off) cleanup of this export file.
+			wp_schedule_delete_personal_data_export_file();
+
 			/**
 			 * Fires right after all personal data has been written to the export file.
 			 *
diff --git a/src/wp-admin/includes/upgrade.php b/src/wp-admin/includes/upgrade.php
index 914113bde00d0..ae095c3df8ee2 100644
--- a/src/wp-admin/includes/upgrade.php
+++ b/src/wp-admin/includes/upgrade.php
@@ -890,6 +890,10 @@ function upgrade_all() {
 		upgrade_700();
 	}
 
+	if ( $wp_current_db_version < 61834 ) {
+		upgrade_710();
+	}
+
 	maybe_disable_link_manager();
 
 	maybe_disable_automattic_widgets();
@@ -2510,6 +2514,37 @@ function upgrade_700() {
 	}
 }
 
+/**
+ * Executes changes made in WordPress 7.1.0.
+ *
+ * @ignore
+ * @since 7.1.0
+ *
+ * @global int $wp_current_db_version The old (current) database version.
+ */
+function upgrade_710() {
+	global $wp_current_db_version;
+
+	/*
+	 * Unschedule the legacy hourly personal data export cleanup event.
+	 *
+	 * Cleanup is now scheduled as a one-off event when an export file is
+	 * generated. See wp_schedule_delete_personal_data_export_file().
+	 */
+	if ( $wp_current_db_version < 61834 ) {
+		$next_scheduled = wp_next_scheduled( 'wp_privacy_delete_old_export_files' );
+
+		if ( $next_scheduled ) {
+			$schedule = wp_get_schedule( 'wp_privacy_delete_old_export_files' );
+
+			// Only remove the recurring event; leave any on-demand single events alone.
+			if ( false !== $schedule ) {
+				wp_unschedule_event( $next_scheduled, 'wp_privacy_delete_old_export_files' );
+			}
+		}
+	}
+}
+
 /**
  * Executes network-level upgrade routines.
  *
diff --git a/src/wp-includes/default-filters.php b/src/wp-includes/default-filters.php
index 4b6d9de25fa11..a8a262cd30867 100644
--- a/src/wp-includes/default-filters.php
+++ b/src/wp-includes/default-filters.php
@@ -445,7 +445,6 @@
 add_filter( 'wp_privacy_personal_data_exporters', 'wp_register_media_personal_data_exporter' );
 add_filter( 'wp_privacy_personal_data_exporters', 'wp_register_user_personal_data_exporter', 1 );
 add_filter( 'wp_privacy_personal_data_erasers', 'wp_register_comment_personal_data_eraser' );
-add_action( 'init', 'wp_schedule_delete_old_privacy_export_files' );
 add_action( 'wp_privacy_delete_old_export_files', 'wp_privacy_delete_old_export_files' );
 
 // Cron tasks.
diff --git a/src/wp-includes/deprecated.php b/src/wp-includes/deprecated.php
index 14f5c24aec914..b8486819a268f 100644
--- a/src/wp-includes/deprecated.php
+++ b/src/wp-includes/deprecated.php
@@ -6533,3 +6533,17 @@ function wp_sanitize_script_attributes( $attributes ) {
 	}
 	return $attributes_string;
 }
+
+/**
+ * Schedules a `WP_Cron` job to delete expired export files.
+ *
+ * This function is deprecated. Cleanup is now scheduled as a one-off event when
+ * a personal data export file is generated, via
+ * {@see wp_schedule_delete_personal_data_export_file()}.
+ *
+ * @since 4.9.6
+ * @deprecated 7.1.0
+ */
+function wp_schedule_delete_old_privacy_export_files() {
+	_deprecated_function( __FUNCTION__, '7.1.0', 'wp_schedule_delete_personal_data_export_file()' );
+}
diff --git a/src/wp-includes/functions.php b/src/wp-includes/functions.php
index 7d71c8c56963d..a9c48ce95ebc5 100644
--- a/src/wp-includes/functions.php
+++ b/src/wp-includes/functions.php
@@ -8457,18 +8457,37 @@ function wp_privacy_exports_url() {
 }
 
 /**
- * Schedules a `WP_Cron` job to delete expired export files.
+ * Schedules a one-off `WP_Cron` job to delete expired export files.
  *
- * @since 4.9.6
+ * Called after a personal data export file is generated so that the cleanup
+ * runs once, shortly after the file is due to expire, rather than hourly on
+ * every site.
+ *
+ * @since 7.1.0
  */
-function wp_schedule_delete_old_privacy_export_files() {
+function wp_schedule_delete_personal_data_export_file() {
 	if ( wp_installing() ) {
 		return;
 	}
 
-	if ( ! wp_next_scheduled( 'wp_privacy_delete_old_export_files' ) ) {
-		wp_schedule_event( time(), 'hourly', 'wp_privacy_delete_old_export_files' );
+	/** This filter is documented in wp-includes/functions.php */
+	$expiration = apply_filters( 'wp_privacy_export_expiration', 3 * DAY_IN_SECONDS );
+
+	// Run shortly after the file is eligible for deletion.
+	$run_at = time() + (int) $expiration + MINUTE_IN_SECONDS;
+
+	$next_scheduled = wp_next_scheduled( 'wp_privacy_delete_old_export_files' );
+
+	// Avoid stacking events; keep the earliest one that covers this file.
+	if ( $next_scheduled && $next_scheduled <= $run_at ) {
+		return;
+	}
+
+	if ( $next_scheduled ) {
+		wp_unschedule_event( $next_scheduled, 'wp_privacy_delete_old_export_files' );
 	}
+
+	wp_schedule_single_event( $run_at, 'wp_privacy_delete_old_export_files' );
 }
 
 /**
@@ -8481,6 +8500,7 @@ function wp_schedule_delete_old_privacy_export_files() {
  * layer of protection.
  *
  * @since 4.9.6
+ * @since 7.1.0 Reschedules a follow-up one-off cleanup if any unexpired files remain.
  */
 function wp_privacy_delete_old_export_files() {
 	$exports_dir = wp_privacy_exports_dir();
@@ -8503,12 +8523,28 @@ function wp_privacy_delete_old_export_files() {
 	 */
 	$expiration = apply_filters( 'wp_privacy_export_expiration', 3 * DAY_IN_SECONDS );
 
+	$now                  = time();
+	$next_expiration_time = 0;
+
 	foreach ( (array) $export_files as $export_file ) {
-		$file_age_in_seconds = time() - filemtime( $export_file );
+		$file_mtime          = filemtime( $export_file );
+		$file_age_in_seconds = $now - $file_mtime;
 
 		if ( $expiration < $file_age_in_seconds ) {
 			unlink( $export_file );
+			continue;
 		}
+
+		// Track the earliest expiration of files that survived this pass.
+		$file_expires_at = $file_mtime + (int) $expiration;
+		if ( 0 === $next_expiration_time || $file_expires_at < $next_expiration_time ) {
+			$next_expiration_time = $file_expires_at;
+		}
+	}
+
+	// If any non-expired files remain, schedule a follow-up cleanup for them.
+	if ( $next_expiration_time > $now && ! wp_next_scheduled( 'wp_privacy_delete_old_export_files' ) ) {
+		wp_schedule_single_event( $next_expiration_time + MINUTE_IN_SECONDS, 'wp_privacy_delete_old_export_files' );
 	}
 }
 
diff --git a/src/wp-includes/version.php b/src/wp-includes/version.php
index 934e5d0bb5369..364e97f70ce2a 100644
--- a/src/wp-includes/version.php
+++ b/src/wp-includes/version.php
@@ -23,7 +23,7 @@
  *
  * @global int $wp_db_version
  */
-$wp_db_version = 61833;
+$wp_db_version = 61834;
 
 /**
  * Holds the TinyMCE version.