The DBS Renewal notification that is set to send out emails based on the DBS renewal date will be triggered by any of the expiry dates on the Background Checks page. It will not only be triggered by the Enhanced DBS check.
As a workaround, please add a date in the Renewal Date field only for the background checks you wish to be notified of. The date can be added to the Notes field in order to keep it on the system.
Go to the employee's profile.
Go to Employment and click Background Checks.
Click a background check and enter the date in the Renewal Date field.
Click Save.