First, cancel your automatic renewal (see associated FAQ entry).
Once the current subscription expires, reapply for premium with the new information. This is for your security that we do not allow changes to billing information.
To further explain, we no longer store any of your personal information on our end. It's either handled by our payment processor, BluePay, or via PayPal. If you purchase a subscription, it's handled as a single transaction with recurring payment agreements. If any of the payment information changes you'll just want to cancel automatic renewal and wait for the subscription to lapse. Once it does, you can sign up again with the updated details.