Diagnosis
This is an audio delay (lip-sync) issue caused by wireless audio processing. It's most common when the HomePod is the default audio output for the Apple TV.
How to Fix It
On your Apple TV, go to Settings > Video and Audio > Audio Format. Change the format from "Auto" to "Dolby Digital 5.1" or "Stereo." The "Auto" setting can cause variable delays.
If That Didn't Work
On the same Apple TV settings page, find "Wireless Audio Sync" and run the calibration tool. It uses your iPhone's microphone to measure and correct the delay. Ensure the room is quiet during this process.
Heads Up
If you're using the HomePod in a stereo pair as the default output, wireless sync is more critical. Also, ensure both your Apple TV and HomePod are on the same Wi-Fi network and updated to the latest software versions.