Change Payment Method
How do i change my payment method for Apple TV?
Also, i have an older account. Does it include the Apple Tv that was just sold to me by Spectrum Cable?
Apple TV 4K, tvOS 13
Read here: Change, add, or remove Apple ID payment methods - Apple Support
The age of your account is not important. If you get shipped a new Apple TV box, then that may qualify for the offer. Set it up, sign in with your Apple ID account, then try to redeem the offer, see if you are eligible. Apple TV+ - One Year Offer - Apple