Delete payment card and add new payment card

You may --> Change, add, or remove Apple ID payment methods - Apple ...

Before changing or adding new., ensure the following

Check the following

1. The payment method that you are adding is of the same country as that of App Store Country on your iPhone
2. You have valid payment plan / debit / credit card from an authorised bank from the same country
3. Payment methods that you can use with your Apple ID - Apple Support
4. Learn more about family purchases and payments.
5. Please check if your Debit/Credit card is valid internationally

Cannot delete payment card or add a new card so I can make a payment on my account

You need to add the new card first, make it the primary, then delete the old card.