This how-to article explains how to set up email notifications for users with pending approvals.
Navigate to the Notification Assistant for Jira configuration screen.
Choose to add a new notification or edit the notification you are currently using for approvals.
In the JQL Expression field write your JQL query where the approvals appear. It must include the approvals=pending() section or whichever field you use to track approvals. Beyond that, you can broaden or narrow it down to your liking. In our example we use: Project=ABC and Approvals= pending()
In the "Recipients" field choose the custom field that you use to track approvers. In our example we chose the "Approvers" field.
Fill in the rest of the information as you see fit.
In step 3, you can also use a JQL filter, just be sure it includes the approvals = pending() or whichever field you use to track approvals with the pending() function.