Hello Wesley,
Welcome to Apple Support Communities. We understand that your external drive does not appear to be mounted although connected to your Mac.
Try another USB port if possible. That may help to isolate this to either the external drive or the USB port.
Have you used this external drive with this Mac or another computer previously? Does the external drive appear in your Mac storage? You can find that from the Apple () > About This Mac > Storage. If not, does it appear in Disk Utility (Finder > Applications > Utilities > Disk Utility). If you see it in Disk Utility, you may need to reformat it. Have a look at Erase and reformat a storage device in Disk Utility on Mac.
Have a great day!