Once the external hard drive does not show up on your Mac, you ought to check if the connection goes well. Either try another adapter or cable to connect the drive to your Mac, then wait to see if the drive shows up on your computer. If not, insert the drive to another machine and see whether it shows up there.
Suppose that the drive shows up on another machine, it's your Mac making trouble. You can reinstall macOS to fix this issue. If the drive doesn't show up on other machines, it indicates your external hard drive goes wrong. For further storage purposes, you'd better get a new drive.
For detailed info, please read: Fix External Hard Drive Not Showing up or Recognized on Mac