To redeem the offer, you have to sign up and start a subscription. The regular signup has a 7 day trial. The offer with new Apple devices should show a year offer, on that new device in the TV app. After the free period, there will be monthly fees, if you are still subscribed by then.
Here’s a guide: Apple TV+ - One Year Offer - Apple
If you qualify, and if you did as described in the guide, and you still do not get to see the year offer, then contact Apple Support. They can assist in getting you the service, if needed using activation codes.