After each step, see if you can connect to the appleTV.

• Verify that the iPad and the AppleTV are on the same SSID on the wireless network (settings -> general -> network)
• Verify that airplay is turned on on the appleTV (settings -> airplay)
• Verify that airplay is turned on on the iPad (settings -> airplay)
• Restart the iPad
• Restart the appleTV (menu)
• Update the appleTV if updates are available (menu)
  • This may take a while
  • Reset the appleTV to factory defaults [ONLY IF YOU DO THE FOLLWING]
    • Write down the current name of the appleTV so you can restore it
    • Someone knows the password to the wireless SSID of the iPad
    • Once you verify that, do these steps:
      • Restore factory defaults (menu)
      • Connect to the same wifi as iPad
      • Turn on airplay
      • Rename the appleTV to the old name

Also see this article: https://support.apple.com/en-us/HT204291