If your external hard drive is not mounting on your Mac, there are a few steps you can try to resolve the issue:
1. Check the connections: Ensure that the USB cable or other connections between the external hard drive and your Mac are secure and properly connected.
2. Try a different port: Try connecting the external hard drive to a different USB port on your Mac. Sometimes, a port may be faulty and switching to a different one can help.
3. Use Disk Utility: Open Disk Utility, which is located in the Utilities folder within the Applications folder, and see if the external hard drive is listed. If it is, select it and click the "Mount" button. If the drive is not listed, try clicking the "First Aid" button to run a repair on the disk.
4. Check for driver updates: If your external hard drive came with a driver CD or software, check to see if there are any updates available for your Mac. Installing the latest drivers can sometimes resolve issues with mounting external hard drives.
5. Try on another Mac or PC: If you have another Mac or PC available, try connecting the external hard drive to it to see if it will mount. This can help determine if the issue is with the hard drive itself or with your Mac.
Further, I suggest you to check the below link for detailed steps to be followed in each method above.
If nothing works then, there may be a hardware problem with the external hard drive. In this case, you may need to contact the manufacturer or a professional data recovery service provider for further assistance.
[Link Edited by Moderator]