Is there anyway to play music on my MacBookPro through to my Apple TV Without having to mirror the screen it?

How do I play music through Apple TV? I'm having issues with connectivity the networks are the same. The only way I can play audio through my Apple TV is if it is mirrored from my laptop to the Apple TV. Is there anyway to play music through my Apple TV Without having to mirror it?

After I type in the four digit code I am unable to connect to my apple tv this dialog box pops upon my screen.