I have purchased movies in my library on iPad but they don’t show up on tv. How can I find them on tv?

On what device do you have the Apple TV app, as accessible on your TV?

List of Apple TV app-supported devices - Apple

Some smart TVs may have the Apple TV+ app instead of the full Apple TV app. The difference is that the former doesn’t have access to ‘buy’ content (nor third party channels): Apple TV+ content only. Get the Apple TV app or Apple TV+ app on your smart TV or streaming device - Apple Support. Which edition is available to your device, depends on the exact model (and thereby age/​OS version/​high-endness).

On AppleTV they should be in the AppleTV App and your library if I recall. Unless you're running an older tvOS and AppleTV? That's how it is on my AppleTV 4K Gen 2.