This happened to me when I had to report my credit card lost. To enter new credit card information:
* Tap on your image/icon in the upper right corner of the App Store app.
* Then, on the Account screen, tap on your name.
* Then tap on Payment Information.
* Enter updated credit card information.
However, I have to say that the user interface we both experienced is abysmal and clownish. In my case, it is also exceedingly annoying that I can't even download things I've already purchased until I get my new credit card.