I notice that I'm not the only one having issues with 'No Service' on the iPhone 7 after the latest update. It started getting bad 2 days ago and I could not connect to my cellular network. I tried:
Turning it off and waiting for a minute. Upon restart, I'd connect for about a minute before I received another 'Cellular Update Failed' notification and went back to having no service.
Network Reset. Upon restart my iPhone didn't even connect to the cellular network for the brief period like it did after the restart.
I saw another person say they took theirs into an Apple store and I plan to do that tomorrow.