My phone is updated. It isn’t asking any updates but my cellular service is off. What should I do?

Start here→If you see No Service or Searching on your iPhone or iPad - Apple Support and note that one of the last steps is to contact your carrier.

If you have an iPhone 7, also see→iPhone 7 Repair Program for "No Service" Issues - Apple Support

If neither of those links address the problem:

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
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.