Under the Finder menu - Finder Preferences, then General tab.
And look at "Show these items on the desktop:"
If "External disks" is not checked, then check the box. Any mounted external drives should show up immediately.
If the box was already checked, then "uncheck", restart your Mac, and then check that box again. Should reset, and show your external drives.
Does that fix?
I don't particularly care to show any hard drives on the desktop, but I often use the drive's icons under Devices on any finder window.