Why won’t it let me edit my new payment card.
It will not let me edit my payment method or will it let me remove my credit card so to add a new one for payment.
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Are you following the steps mentioned in the related article?
Change, add, or remove Apple ID payment methods - Apple Support
You can only remove the old payment info, if you set up your new one before, especially if you have ongoing subscriptions.
If this does not work either, you'll have to contact the official Apple Support and ask them to look into your personal settings, to find the issue. They are the only ones that have access to other users data.
Contact Apple for support and service - Apple Support