There no “ loyalty card” choice in my wallet. How do I put loyalty cards in my Apple wallet?

Loyalty cards can only be added to the Wallet if the company gives you that option through the use of their app or possibly an email link they have sent you. Anything added to your wallet needs to be approved by the issuing body of the card, whether it is a Credit/Debit card, Airline Tickets, Boarding Pass, Show Tickets, and even Loyalty cards.

Use passes in Wallet on iPhone - Apple Support

Your state must allow the option to add your Driver's License to the Wallet. So far, just a few states have passed legislation that would make that possible, with many more still working to pass legislation.

What are you trying to add? Are trying to add loyalty/rewards card for a gas station, grocery store, hotel chain or what exactly?

Are you trying to add a state issued ID or a driver’s license or again, what exactly are you trying to add to your wallet?