You can change or update the credit / debit card details you use for payment anytime from within Timetastic.
Payment and Invoicing is an Admin function so only users with admin rights can do the following:
Select SETTINGS > BILLING from the main menu:
From the billing page you can click the green button to update your card details:
The update is instant, meaning your next and subsequent payments will be charged to your new debit or credit card.