Streaming to Apple 4K TV

Not sure why you would want to bring your iPad into the mix, when that isn’t needed. Get the Movies Anywhere app for tvOS to stream directly on Apple TV.

But they say that AirPlay screen mirroring is available.

Smart TVs & streaming devices - Movies Anywhere supported devices - Movies Anywhere Help

“AirPlay: Movie playback is available using AirPlay Mirroring from a compatible computer or device on the same Wi-Fi network.”

You need to speak to the developer of the app to see if they allow Airplay to work with their app. If they do, then you are good to go!