I need to add a new credit card to my account

Log into your account in the App Store/iTunes and you should be able to change/verify it there. Or you can click the blue Edit payment methods in the article below. When signed in and the page loads, you will be on the credit card page. After updating that, click the Go Back button at the lower left and you will be on the address page. If you have a subscription, you need to add the new card, and then promote it to the primary payment method before you can remove the old card.

Apple ID payment information - change.