Error -15007

Followed your suggestion...got to 1) and didn't need to go further! Thanks!

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 computer.

I tried but it didn't work. Any other suggestions?

Point 1) solved it for me too.

I found the answer to this error was on Apple TV device verification. I had turned it on, which it didn't like.

Settings > AirPlay > Require Device Verification - switch it to Off.