The easiest is to cast the screen. That requires a compatible TV but works great, and you can still control the app from the phone or tablet.
Edit: I just realized that does not quite answer your question because I do not know of a way to have the app actually run on the TV and get inputs from the TV's touch screen.
It may be possible if the TV is attached to a Chromebook which can run Android apps. The problem will be to get the TV's touch screen inputs into the app. Even though, personally, I think it is easier to cast the tablet's display to the TV and use the touch screen on the tablet, only use the TV as a second display.