Yes! You will have to go to your Account Settings and click Update Billing Information.
You will need to do this if you change bank cards and wish to continue with your current subscription plan without having to resubscribe. Otherwise, you will return to being a free member once your current payment period expires and will have to go through the payment process again.
For older members: if the plan you are on is not available as an option any more, is it vital that you update your billing info before your card expires. If you fail to do so, you will return to being a free member when your subscription period ends and will no longer be able to get back on the previous plan.