Is it possible to completely remove my current credit card information from my account subscription?
It's not possible to manually remove credit card information from your Zendesk account. If your payment method is a credit card, Zendesk will always require a card in place on your account.
However, you can replace the existing card details with another credit card. For information on how to do it, see this article: How can I change the credit card on file for my account? [Video]
If you are interested in an alternative payment method for your subscription, reach out to your account representative directly or contact the Zendesk Customer Support team.