Yes, it is possible to use the free space on your external HDD for Time Machine backups, but you will need to reformat the disk to a compatible file system. Time Machine requires a specific file system format called "Mac OS Extended (Journaled)" or "APFS" (Apple File System) for macOS 10.13 High Sierra and later.
Before proceeding with the reformatting process, please note that reformatting will erase all the data on the external HDD. Therefore, it's essential to make sure you have a backup of any important data on the drive before proceeding. Here's how you can reformat the disk and use it for Time Machine backups:
1. Connect the external HDD to your iMac.
2. Open "Disk Utility." You can find it by going to "Applications" > "Utilities" > "Disk Utility."
3. In Disk Utility, you should see a list of available drives on the left-hand side. Select your external HDD from the list.
4. Click on the "Erase" button at the top of the Disk Utility window.
5. In the erase dialog box, choose the desired format for the disk. If your iMac is running macOS Monterey, it is recommended to select "APFS" as the format. If you're running an older version of macOS, choose "Mac OS Extended (Journaled)."
6. Give your disk a name, and then click on the "Erase" button to begin the reformatting process. Please be aware that this will erase all data on the drive.
7. Once the reformatting process is complete, you can close Disk Utility.
8. Go to "System Preferences" on your iMac.
9. Click on "Time Machine."
10. Click the lock icon at the bottom-left corner of the Time Machine preferences window and enter your administrator password to unlock the settings.
11. Click on "Select Backup Disk."
12. You should see your newly formatted external HDD listed. Select it and click on "Use Disk."
13. Time Machine will now use the available free space on your external HDD for backups.
Remember to keep your external HDD connected to your iMac if you want Time Machine to perform regular automatic backups.