Delete old and add new credit card details

Start here:

Change, add, or remove Apple ID payment methods - Apple Support

If you can't remove your last payment method or use no payment method with your Apple ID - Apple Support

If you can't change your method of payment using your phone, then do so here:

Apple ID: Manage your Apple account - Apple Support

If it won't allow you to delete a card, it's because you have an active subscription. You can cancel your subscriptions, then update your payment info. When you cancel a subscription, you'll be able when the subscription will end. You'll simply start the subscription before that end date.

Update your payment online at appleid.com or in settings of an iOS device>tap name>tap payment info. On a Mac, open iTunes app>account>view account>payment info