What kind of update is it saying that you need? If you need to update the operating system (iOS), and your iPhone is compatible with a more recent version of iOS, see:
Update your iPhone or iPad - Apple Support
If you can't update the phone wirelessly (by connecting it to power, and, via Wi-Fi, to the Internet), you may be able to update it "manually" with the help of iTunes or Finder running on a Mac or a Windows PC.
It may be that your phone company (carrier) wants you to update carrier settings. I'm not sure if this would happen during the process of activating your SIM (physical SIM or eSIM) … carriers can push out their updates at any time. If you need to install one of those (a different thing than a whole new version of iOS), see:
Manually update your carrier settings on your iPhone or iPad - Apple Support