There are no updates for your Apple TV unless you have the Apple TV 4, even so changing your TV shouldn't affect how your Apple TV works unless you have some sort of HDMI issue with the new TV or cable.
Did you check whether you should be able to see video when air playing this content. If you should be able to...
- Check AirPlay is turned on on the Apple TV (turn it off and on if it already is)
- Check that both devices are on the same network (Settings > Wifi, on the mobile device and Settings > General > Network, on the Apple TV).
- Restart the Apple TV (Settings > General > Restart).
- Restart the Apple TV by removing ALL the cables for 30 seconds.
- Restart your router. (Also try removing it’s power cord for at least 30 seconds)
- Restart your mobile device.
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.