Hi Dsk23,
welcome to the Apple (user-to-user) Community.
Re: How can I delete a card and add a new one?
Wondering where you use the credit card ... Apple ID account / Apple Pay purchases / ? Apple Card
Eg:
Your Apple ID is the one account you use to access Apple services like the App Store, Apple Music, iCloud, iMessage, FaceTime, and more. It includes the email address and password you use to sign in as well as the contact, payment, and security details you use across Apple services.
With an active Apple subscription: seems we just have to add a new card, before we can delete the old one:
For payments to Apple : Apple ID account:
Check which payment methods Apple can accept in your country or region:
Payment methods that you can use with your Apple ID - Apple Support
How to add an Apple ID payment method:
Add a payment method to your Apple ID - Apple Support
How to delete an Apple ID payment method:
Remove a payment method from your Apple ID - Apple Support
How to change an Apple ID payment method:
If you need to change or update your Apple ID payment method - Apple Support
NB: You may need to allow 24 hours for updates to come into effect.
or
Restarting your device may help you view recent changes.
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For Apple Pay: (Payments Apple transfers to merchants / websites etc. using your card-provider account.)
How to: Change or remove the payment cards that you use with Apple Pay - Apple Support
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As this is actually the discussion area for the Apple Card (Apple's credit card) community:
How to: Add or remove a bank account for online Apple Card payments - Apple Support
How to make Apple Card payments - Apple Support
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All the best :-)