You can update your credit-card information at any time by going to Settings, then clicking on the Account/Payment option.

From there, click on 'update billing info'

Or, simply click here: https://www.chess.com/settings/payment

Here you can change the payment method to a new card, or if you want to switch to something else, such as PayPal for example, you can update via choosing your plan at the membership page.

If you already are using PayPal you must log in to PayPal in order to make any changes.