No service

You need to restore the phone using your computer. Use iTunes if you have a PC or a Mac with MacOS 10.14 or earlier, or Finder with Mac OS 10.15 or later. After restoring you can restore your backup.

Restore your iPhone, iPad, or iPod to factory settings - Apple Support

Do not restore! This error indicates a hardware issue. See iPhone 7 Repair Program for "No Service" Issues - Apple Support

Well, actually, not so. The message "Error - an update is required to use cellular data on this iPhone” means that the baseband firmware on the phone is corrupted. To verify this go to Settings/General/About and look at the Modem Firmware version - it will be blank. This is not the same problem addressed by the repair program, which is for a broken Wi-Fi antenna connection in the phone, and does NOT display that error message. Instead, it will just show “No Service” or “Searching” in the status bar.

To fix it the phone for that specific error the phone must be restored from a computer, which reinstalls the baseband firmware.

If an iPhone 7, what do you see when you go to Settings > Cellular?

Have you tried Reset Network Settings?

No!!!!!!!!!!! Do not restore for this issue as they are seeing "Error - an update is required to use cellular data on this iphone" under Settings > Cellular.

While your intentions are good, your information is incorrect for those model iPhone 7's affected. Source: directly from Apple internal guidelines.

Not just my intentions, but my information is accurate. As the original poster will discover in the fullness of time.