Pair AirPods to tvOS 11 Using the public beta version of tvOS 11 on an AppleTV 4th-generation.

How to pair my AirPods ear buds? 

This new version 11 is supposed to make easy work of pairing. But when I open the AirPods case next to the Apple TV, nothing happens. When I go to Settings > Video and Audio > Audio Output, all I see listed is "Apple TV" both when case is open nearby and when wearing the AirPods.

These AirPods are already paired with both my iPhone and Mac, without problems.
Pick up your AirPods charging case and open it.
Press and hold the pairing button on the back of the case.
Launch Settings on your Apple TV
Click on Remotes and Devices.
Click on Bluetooth.
Select your AirPods from the list.

https://support.apple.com/en-us/HT207010

https://discussions.apple.com/message/31128330#31128330

https://www.imore.com/how-pair-your-airpods-apple-tv-android-and-other-bluetooth-devices