First your should redeem the offer in the TV app on your new device.
Apple TV+ - One Year Offer - Apple
Once you have the Apple TV+ subscription, it will be available on all your devices that have the Apple TV app and are signed in with your Apple ID account that has the subscription.
Depending on your model TV, the Apple TV app may be available there among its smart apps, either pre-installed or downloadable. If not, then you may have to connect an external streaming device.
Apple TV app-supported smart TVs and third party streaming devices - Apple
All the ways to watch Apple TV+ - Apple Support