If I buy 4K movie from iTunes will it play on 4K on 4K tv?

If you are using airplay to stream the downloaded film from your iPad/iPhone, it would be in 1080P. In order to have it in 4K you would need to be streaming it directly using the TV app on Apple TV hardware or a device that supports the TV app.

Apple TV app - Devices - Apple (CA)

Yes, that will be in 4K, if the TV is officially AirPlay 2-enabled.

4K content can only be accessed on Apple TV 4K or another 4K device that supports the TV app. It is not possible to download content in 4K so anything stored on your iPhone/iPad would be in 1080P and that is what would be streamed using airplay.