Apple TV subscription playback on home TV

If your smart TV doesn’t offer you to have or install the Apple TV app, then another option is to connect an external HDMI streaming device that supports the Apple TV app, bypassing the TV’s smart app system. That can be an Apple TV box, Roku, Fire TV, PlayStation (4, 5), Xbox (One, One S, X, S), ‘Chromecast with Google TV’-dongle, or Nvidia Shield TV, or select external cable/satellite TV tuner boxes that support apps.

Get the Apple TV app or Apple TV+ app on your smart TV or streaming device - Apple Support

Watch on these smart TVs and third party streaming devices - Apple Support

All the ways to watch Apple TV+ and more - Apple Support

Less convenient, it is also possible to connect an iPhone or iPad to your TV using an HDMI adapter.

Computers (laptops) can also connect through HDMI to a TV as second screen.

Sign into the Apple TV+ app on your TV with the Apple ID/Password you are using on your device. Not sure the model of TV you have, but you would need to find out if it supports Apple TV.