Welcome to the Apple Community.
Try the following steps, check whether things are working after each step where appropriate, before trying the next.
1. Check AirPlay is turned on on the Apple TV (turn it off and on if it already is)
2. Check that both devices are on the same network (Settings > Wifi, on the mobile device and Settings > General > Network, on the Apple TV).
3. Restart the Apple TV (Settings > General > Restart).
4. Restart the Apple TV by removing ALL the cables for 30 seconds.
5. Restart your router.
6. Restart your mobile device.
I have the same problem. Fully updated 720p Apple TV 2 has no audio with HBO GO. On the same device, on same tv, with same iPad or iPhone. All other apps or mirroring mode WORKS with audio. HBO GO only app with no audio. If I turn on mirroring, still no audio.
I have a newer 1080p model which works fine with HBO GO, but its on another TV. I want to use this on an older 720p TV in my exercise room. I did test move it and it works.
Seems like some sort of big with HBO GO. Surprised it's not reported more.
I am having the same issue when airplay'ing HBOGO from a 2nd gen iPad to a 720 panni that's 6 years old...I hear the hbo intro.. But when it cuts over to the movie.. No sound.. Have restarted the atv3 device and ipad but its not working.. Very frustrating to play your content sometimes.. I may be returning this atv3..
I am embarrassed to admit what was wrong for me: I had to turn off surround audio support on the ATV. I was moving my two units between TV's with different audio support, and the two were not configured for audio the same. On my old tv, only enabling stereo audio fixed HBO Go, because post intro sequence, it would output surround audio data to tv over HDMI and be silent.