Some users have complained that they see the No Service message on their iPhones after upgrading to iOS 9.3. The fix for this issue has not changed and it still remains the same as prior iOS versions. There are a few different options to address this issue.
Turn off Cellular Data
Before proceeding to any complicated solutions, try to switch off the cellular data to “Off” in your settings by going to Settings > Cellular > Cellular Data . Next, put your device to Airplane mode and then turn it off for a minute or so. Power back your iPhone, switch off your Airplane mode and then enable the Cellular data option. This should address the problem.
Restart your iPhone
Try Resetting your iPhone by holding both the Home button and the Sleep/Wake button until you see the Apple logo. Let the device restart and see if the issue has been fixed.
The third and final option although takes a little effort has proved handy in the prior iOS versions when users faced this problem. Switch off your iPhone. Follow Apple’s directions and remove the SIM Card from the SIM tray. Next, Switch on your iPhone, unlock the device and insert back the SIM card back to the device. You should be good to go.
Please let us know which options worked for you or if you found a different tip to help you with this issue. Good Luck!