How do I activate my existing ATT cellular service to my new IPhone 13

Either move the nano sim card form your previous phone to the new one, or setup your service in Settings->Cellular.

More information here: link-> Set up cellular service on iPhone - Apple Support

If you did not have your phone preordered to activate to the eSim in your new phone, contact AT&T and have them activate the eSim to your telephone number.

Edit: If your previous iPhone was not a 5G iPhone, and you prefer to use a physical sim card, get a new sim card from AT&T which has been provisioned for 5G service.