Why is my Apple TV app not working on iPhone?

The TV app on iPhone or iPad needs internet access, to show anything other than the local library.

• Through Wi-Fi, the TV app should have regular internet access.
• On cellular, the TV app would need extra permission to use cellular data. Settings﹥Cellular﹥[scroll down to apps list] TV app﹥

have you tried to force restart the iPhone?

Force restart iPhone - Apple Support

What do you mean “not working”? What happens when you try to use the app? Do you get an error message? What does it say exactly?