When I Get Apple TV free from my new iPad can I also watch it on my TV

Your Apple TV+ subscription is usable on any of your devices that have the Apple TV app, when signed in with the same Apple ID account.

It is Apple TV+ that has a free year -- that is not the same as Apple TV. Apple TV+ - Apple

I watch my free subscription on my TV by using a Roku device. How you do it depends on what TV you have (some newer TVs have an Apple TV app available directly on the TV).