Your subscription is grandfathered as a six-month sub. It can’t be edited by you to have new payment information, so when you cancel it or it fails to renew, that will be the end and you will need to purchase a new license. (Maxon has monthly or annual subs, but no six-month subs.)
During the month of September, your subscription billing will be moved from Authorize.net to Digital River. In most cases, nothing will need to be done by you for that to happen. When it does take place you will receive an instructional email.
Before your subscription renews, you will need to install ZBrush using the Maxon App. That way it will be able to use Maxon’s licensing system and see the payments being made there. Your legacy installation will stop working the day that the renewal happens because the legacy system can only see Authorize.net’s billing.