How do I get the Apple TV app on my sony tv?

if your model is listed here it should be supported Apple TV app - Devices - Apple

if it is not then you will have to purchase the appletv box Apple TV 4K - Apple

Select models TV, as indicated in the list, support the Apple TV app.

Other models TV will have to connect an Apple TV app-supported HDMI device to get this app on the TV.

List of Apple TV app-supported smart TVs and third party streaming devices - Apple

All the ways to watch in the Apple TV app - Apple Support

Watch on your TV

Apple TV (4K, HD, and 3rd generation) ﹥

Smart TVs ﹥

Gaming consoles ﹥

Streaming devices ﹥