How do I connect my AirPods to my Apple TV?

Give the following a try:

1. Put your AirPods in their charging case.
2. Press and hold the button to establish a pairing connection.
3. Hold down the button until the LED flashes. This should indicate they are ready to pair with another device.
4. Open Settings on the Apple TV.
5. Using the Apple TV remote, select Remote Devices.
6. Select Bluetooth.
7. Your AirPods should appear in the list of available Bluetooth devices.
8. Select them.