An update is required to use mobile data on this iPhone

There are several possible causes for this problem. Here is the easiest→If you see "Software update is required to connect to your iOS device" on your iPhone, iPad, or iPod touch - Apple Support

If that isn’t the problem→If you see a Cellular, Ultra Wideband, or Apple Pay Issue message after an iOS update or restart - Apple Support

This can also be cause by corrupted modem firmware. 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 or the link in If you see a Cellular, Ultra Wideband, or Apple Pay Issue message after an iOS update or restart - Apple Support

Update your carrier settings on your iPhone or iPad

Manually update your carrier settings on your iPhone or iPad - Apple Support