Hello tomxmr,
Thank you for using Apple Support Communities!
We understand from your post that while on a call you are unable to enable AirPlay to listen to music on your Apple TV. AirPlay is enabled and you are playing music before you make or receive a call, AirPlay will continue to play your music on the Apple TV during your call. If you pause your music and you make or receive a call, you can play your music again while on the call. If AirPlay is disabled and the AirPlay device is not selected, you will not be able to select your device while on a call. You will have to select it either before or after your call.
You can leave feedback about this feature here: Product Feedback - Apple
Best Regards.