Apple TV+ 3-month free subscription not working on my TV

Follow the instructions in the Apple TV+ page called Get 3 months of Apple TV+ for free.

In the questions and answers down the bottom of the page you will see this:

I bought a new Apple device that came with three months of Apple TV+ for free. How do I activate my subscription?

You can activate your free Apple TV+ subscription after you set up your new Apple device. Simply follow the steps outlined above. Or visit support.apple.com for more information.

The steps mentioned in this passage as "above" are:

Redeem 3 months of free Apple TV+ now. 

You can start your free three-month subscription to Apple TV+ after setting up your new Apple product. Here’s how to redeem your offer. 

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 you launch the app. If not, go to the Apple TV+ tab, where you’ll see the offer. 
4. Tap Enjoy 3 Months Free.

On Macs, users have to sign in separately to the Apple TV app. Do so through the menu Account, or else through the icon at the bottom of the side bar on the left.

Which offer are you referring to? Check the eligibility requirements as usually they are only for new subscribers. If you had used a free trial previously, you would not be eligible.