To change the bank card used for your subscription, you will need to make a purchase on the website.
You can save a new bank card while confirming payment. Make sure to check the box:
“I authorise Ingenico to store my financial details in a secure way, so that I will not have to enter them again for future orders with this merchant.”
Then click on your profile icon, “My account,” and the “Payment information, wallet & gift cards” tab. You will then be able to select the card you wish to use to pay for your subscription.