According to: Get Apple TV+ free for one year.
Redeem your free year of Apple TV+ now.
- You can start your free one year subscription to Apple TV+ after setting up your new Apple product. Here’s how to redeem your offer:
- Turn on your new Apple device and sign in with your Apple ID.
- Open the Apple TV app. Make sure your device is running the latest version of iOS, iPadOS, tvOS, or macOS.
- 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.
- Tap Enjoy 1 Year Free.
Although you are indicating that you have just purchased a new computer, your post indicates that you are using macOS 10.14, which is not the latest version of macOS. If that is true, you do not have the TV Application. If you don't want to upgrade to macOS 10.15 Catalina, you should be able to access the offer by using Safari and signing in to: Apple TV+ with your Apple ID.