Hi,
Sorry to hear you are having issues with your payment method tied to your Apple ID.
Do you also use this card for Wallet and Apple Pay? If so, do you have it linked from Apple Pay to your Apple ID?
To confirm, you would go to Settings > Name > Media & Purchases > View Account > Manage Payments.
The primary payment listed would say Apple Pay.
If it is not linked with Apple Pay, it would just list the last four digits of the card number.
If a payment method is linked to Wallet and also your Apple ID, any changes to the billing address, card number and expiration, etc would need to be updated in the Wallet app.
You would not be able to update the billing info for your Apple ID in Payment & Shipping or Media & Purchases.
If the old card is still associated to Wallet, remove it and add the updated one.
Settings > Wallet & Apple Pay > click on the affected card > scroll to the bottom and click Remove this Card.
You can then add the new card to Wallet.
Once you remove the affected card from Wallet, your payment method for your Apple ID will revert back to the card on file before linking it with Apple Pay.
To update the payment method, go to Settings > Name > Media & Purchases > View Account > Manage Payments
If the issue is unrelated to Apple Pay, are you receiving an error message that your payment can’t be used within the iTS?
If you see the old card and expiration listed, i would recommend going to the Apple ID website to update the payment: https://appleid.apple.com/
https://support.apple.com/en-us/HT201266
https://support.apple.com/en-us/HT205583
Hope this helps!