I am unable to remove my old card from my Apple Account

Any and all active subscriptions would need to be cancelled and expire before you can remove the card on your account, if it's the only one.

Best is to add a new card, and once it's been successfully added, remove the old one.

If you must remove your exiting card without adding a new one, then make sure all your subscriptions have been cancelled and have expired before attempting to remove it.

click here ➜ If you want to cancel a subscription from Apple - Apple Support

You don't need to cancel any subscription.

To find out how to remove a payment method, and what to do if you can't remove your last payment method or use no payment method with your Apple ID, read this article ➔ Remove a payment method from your Apple Account - Apple Support

Unexpired subscriptions and Family Sharing organizers must always have a payment method present. To edit the cards used for those you may need to first add the new card and move it to the top payment method position before removing the old card (see: If you need to change or update your Apple Account payment method - Apple Support ).