hello. My name is***** can help you with your question.
The easiest way to do this would be to go to your Kindle account on your computer web browser. Your Kindle account is the same as your Amazon account so just go to Amazon.com and then log into your account there with your username and password ***** select account settings and then payment methods. When you get there you can remove the previous payment method and add your new credit card and make it the default. Please let me know if you still have question.