To update your payment method you need to remove the existing credit card from your account, under "My Account - Saved Cards - delete"
Then add the new payment method.
Please note, although there is an 'edit' button, you cannot edit the card, you must delete the old one and add a new one, even if it's only the date on your new card, that has changed.
(Your credit card is automatically saved as your default payment option, if you wish to remove it, you can do so through the "Saved Cards" option in your account. This option is not available for AutoDelivery customers as per the Terms and Conditions of the AutoDelivery Policy)