Restart Phone

Try first to optimize the range of the mobile network, see this Apple article:

If you see No Service or Searching on your iPhone or iPad

If you see No Service or Searching on your iPhone or iPad - Apple Support

Charge the battery > 70%

Then see -> If you can't activate your iPhone

If you can't activate your iPhone - Apple Support

One additional possibility: Go to Settings/General/About and look at Modem Firmware. Is the entry blank? If it is you need to reinstall it by restoring the phone to factory settings, then restoring a backup. Back up the phone first, of course:

1. How to back up your iPhone, iPad, and iPod touch - Apple Support
2. Restore your iPhone, iPad, or iPod to factory settings - Apple Support - follow the instructions to restore using your computer, do not using Settings/General/Reset (which is not included in those instructions)
3. Restore your iPhone, iPad, or iPod touch from a backup - Apple Support

If the modem firmware DOES have a value you may have a hardware problem. The first step is what I just posted, but after that you need to contact Apple support using the Get Support link at the top of this page.