How to Fix an External Hard Drive Not Working on My Mac?

Based on your trouble, you should check the connection problem first. You can try to connect your drive via an alternative USB hub, cable, port, or so. If this fix fails to solve your trouble, head to ensure the External Disks option is checked in Finder Preferences. 

Here's how to check if the External Disks option is checked in Mac Finder Preferences: Finder > Preferences > Sidebar > Devices > External Disks.

Some drive comes with write-protection enabled by default for data security which responds to you that the USB flash drives not working on your computer. All you need to do is switch the write protection from one side to another.

Hope you good luck~