Q: Can we connect apple tv4 to external audio receiver and listen to music when the tv is off??

There is no independent audio out, so you would need something that splits out audio from the HDMI connector.

tt2

I don't know for certain. If it is possible at all it will need some third party hardware. Turning off the feature that lets you Turn on the TV with the remote might also let you shut down the screen while not putting the device into sleep. I could test when I have access to my device later.

tt2

Turning off my TV while Apple TV is playing content doesn't appear to force the device to shut down. However the only way to know for sure is to try it. I don't have, or need, an HDMI audio splitter so I will leave that experiment to others.

tt2

Purchase a HDMI splitter (e.g. Best Buy) .   One goes to TV, other to Receiver.  Play music, then turn off TV with your TV remote.  The Apple TV will continue to play the music.  Works for me.

The perfect way for me is connect to my receiver via bluetooth....