external hard drive not showing up on desktop

Does the device show:

• in Disk Utility?
• In "About this Mac..." > "Storage" tab?
• In a window sidebar:

In that image, "Time Machine 2T" is an external hard drive,

As shipped, the Mac OS is not set to show any devices on the Desktop other than the hard drive. You change that through Finder Preferences:

Change Finder preferences on Mac - Apple Support

Just to close out this thread. What worked for me was reformatting the drive in exfat on the Mac. For some reason it would not accept the pc formatting. I think it was because the standard pc block sizing is not accepted on the Mac. Not sure what block size is accepted, but simply allowing the Mac to reformat the drive in exfat did the trick. Luckily this was a new drive so I didn’t need to save anything but make sure to back up the drive before you reformat it if you have anything you need to keep!

Select it and click Erase. Format as APFS/GUID if you’ll only use with 10.13 Macs or higher, MacOS Extended Journaled/GUIDCif you’ll use with a mix of old and new Macs.

i have a similar issue, formatted in exFat to use on both macos and PC. My brand new drive works on PC but will not mount on my MBP running Catalina 10.15.6

Any help would be appreciated!

Only helpful if you want to use the drive solely on a Mac. If you need to use it on a pc too the drive can be formatted in exFat.