What should you do first if a MacBook Air (13-inch, Mid 2013) does not show the AirPlay Display
menu icon on a network with an Apple TV (3rd generation)?
Reset all of the settings on the Apple TV and rejoin the network.
Startup the MacBook Air from Recovery HD and reinstall OS X.
Download the latest copy of iTunes and restore the Apple TV.
Ensure the “Show mirroring options in the menu bar” preference is enabled.