Hi there, the reason turns your external hard drive not showing up on Mac after the macOS Monterey update is uncertain, since I have never heard that a macOS update would make an external drive not show. The file system factor can also be ruled out provided that you have formatted the hard drive as Mac OS Extended (Journaled), which is fully compatible with macOS Monterey. Yet let's put the culprits aside for a moment and focus on the solutions right now.
Once the external hard drive does not show on your Mac, you should go to check the connection first. Either changing the cable or inserting the hard drive to another machine works fine in the connection test.
Or, restart your Mac and reset NVRAM to see if the hard drive functions normally on your computer.
The third option worth your try is to reinstall macOS, which takes some time but it really works!
If these mentioned solutions fail to make your external hard drive visible on Mac, I dare to speculate if your hard drive is problematic. As we all know a hard drive is always going to fail as expected since every hard drive has its life span. Facing this, you can only restore your files from the backup for a usual working environment and replace the broken hard drive with a new one for storage purposes.
For more info, please visit: Fix External Hard Drive Not Showing up or Recognized on Mac
