Q: Airplay Mirroring Icon Not Showing Up

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. (Also try removing it’s power cord for at least 30 seconds)
6. Restart your computer.

If you are still having problems, the following article(s) may help you.

Troubleshooting AirPlay

Troubleshooting Wi-Fi networks and connections

Recommended Wi-Fi settings

Wifi Diagnostic Software (for Mac users)

You may also find some help on this page, where I’ve collected some of the more unusual solutions to network issues.

When making adjustments to your network for better optimisation, you may find some of the points mentioned on this page helpful.

if it'a the old alu 1g Apple TV then it does not support airplay mirror

Have you tried disabling bluetooth.

I was having the same problem with my late 2013 13" MBP Retina running Yosemite 10.10.4, while all my iOS 8.4 devices were having .  Super simple fix.  If you're running a firewall (in my case, McAfee Internet Security), you need to make sure your home network is set to "Home or Work."  Mine was set to "Public," which clearly blocked Airplay.  Fixed it immediately.

Nice...THIS WORKED....I had been at this for SOO LONG NOW.   Going into Mcafee Preferences and switching from PUBLIC to Home & Work was the solution.  Thank you!