“A couple of months?” You’ll have to be a bit more precise.
The offer is valid for 3 months after first activating your new iPhone. After that, the offer expires.
The offer is for the first registered user (account) of this new qualifying Apple device.
The offer has to be redeemed first on your new qualifying Apple device.
The offer is for Apple TV+, not for Apple TV, which is different.
Read here how to redeem in more detail: Apple TV+ - One Year Offer - Apple
Read here about the conditions: Apple TV+ one year offer - Terms and conditions - Apple
Read here if you have trouble redeeming: If you can't redeem your promotional trial of Apple TV+ - Apple Support