On what device are you trying to subscribe? A few devices are unfortunately excluded from financial transactions at this time. Instead try using a different device for the subscribing part, then continue watching on your primary device.
The value of Gift Cards can be redeemed and thereby transferred to balance on an Apple ID account. That balance can then be used for purchases, renting, and subscriptions.
How to redeem your Apple Gift Card or App Store & iTunes gift card - Apple Support
Check your Apple Account balance - Apple Support
A valid payment method card can be linked to your account. As a pre-authorized payment method, it can be used for transactions with a few clicks, without the need to specify the card details each time. Faster and more secure.
Account balance is always used before card payment methods, so to avoid/minimize the unintended build-up of balance.
Subscriptions require a payment method that supports automatic and periodical charges.
Add a payment method to your Apple ID - Apple Support
Payment methods that you can use with your Apple ID (by country) - Apple Support
Manage your Apple ID (including payment method) on the web - Apple
If you need more assistance, consider contacting the Apple Support staff.