How do I delete a credit card on Apple ID?

or do I have to put a new credit card before I can delete

Yes, see -> Add a payment method to your Apple ID

Add a payment method to your Apple ID – Apple Support (UK)

• If you want to change your card, you need to add first the new card, then remove the old card.

Same method as here -> If you need to change or update your Apple ID payment method

If you need to change or update your Apple ID payment method - Apple Support