Apple TV one year free subscription with new Apple device

You would go into the TV app on that iPhone and once signed in with your Apple ID you should see the offer (steps below for reference)

1. Turn on your new Apple device and sign in with your Apple ID.
2. Open the Apple TV app. Make sure your device is running the latest version of iOS, iPadOS, tvOS, or macOS.
3. The offer should be presented immediately after launching the app. If not, go to the Apple TV+ channel page where you’ll see the offer.
4. Tap Enjoy 1 Year Free.

Make sure you are using the eligible iPhone and not another device. If this was a previous purchase then be aware the offer is only valid for 3 months after device activation. If that has been verified and you are still not able to claim then contact Apple support.