"Contacts" application does not start on Mac OS 10.15.7

Open  (Apple menu) > System Preferences... > Internet Accounts

Determine which, if any, of those accounts use Contacts. Perhaps one or more of them are misbehaving. You can de-select Contacts and see if that changes anything. Other than that I'm out of ideas other than to reinstall macOS: Reinstall macOS - Apple Support.

I understand the Contacts app does not launch.

Please determine if the same problems occur in "Safe Mode": How to use safe mode on your Mac.