Why aren't my iTunes purchases showing on Apple TV?

What Smart TV (make and model) are you using?

Does it support the Apple TV app or the Apple TV➕ app? (note the plus sign).

The Apple TV+ app does not support access to purchases. Only content from the Apple TV+ subscription service.

click here ➜ Watch on Smart TVs and streaming devices - Apple Support

Check other devices to see if they show up there, verify the Apple ID and ensure you are signed in with the same account on the Smart TV. If you still have trouble then contact Apple support.