In a Fail Over event the TPAM users need to access the failed over replica to submit PPM/PSM requests. Typically, the email would be linking to a DNS name (the primary). So when the primary fails, it would update the DNS pointer to be the failed-over replica, so when the user accesses the DNS name it points to the failed over replica appliance. When the primary comes back online, then the DNS would get adjusted back to the Primary.
The '/admin' Mail Agent "Application Page Link" can be configured to be what is required. Using a DNS name that you can adjust to point to the primary (or failed over replica) should allow you to do what you require. Application Page Link: "This address will be used for any links in the email which reference a URL in the appliance. This address should be accessible for anyone receiving email from TPAM."
The DNS names do not need to be used; but if you wish to have the email with a URL that points to a primary when the primary is active, and a failed-over replica when a replica is failed over - using a DNS name in that field is one way to do so.
Please review the option for "Use the same URL for all Application Page links". This is useful so that it eliminates the need to modify each specific email.
Also, enable the mail agent when the Replica has failed over to be able to send email. The mail agent must be started to continue automatic email notifications.
Please review the TPAM 2.5.917 System Administrator Guide in Chapter 13 - Email Configuration
The "Email Notification Configuration" menu in the /admin console