how can i use my gift card to pay for my apple tv subscription

Because this is a subscription you may be required to enter a credit card to guarantee payment. If you redeem your gift card it will add balance to you Apple ID which will then be automatically preferentially used to pay for anything you buy before the credit card itself is charged. This is described in this article --> How App Store and iTunes Store purchases are billed - https://support.apple.com/HT201359

Also make sure it is the right kind of gift and how to redeem it:

"To find out how to redeem your gift card and what you can buy with it, check which type of gift card you have" --> https://support.apple.com/HT204199

Redeeming a gift card transfers that money to to your Apple ID account balance. That Apple ID account balance can be used for subscriptions, regardless of other payment methods (or ‘None’).

What you can buy with your Apple ID balance - Apple Support

Add money to your Apple ID balance - Apple Support

Check your Apple ID balance - Apple Support

What type of gift card do I have? - Apple Support

Redeem your Apple Gift Card (US) - Apple Support

Redeem your App Store & iTunes Gift Card - Apple Support