Hi,
To restore an older iMovie library backup from Time Machine, click on the Time Machine icon, and then" Enter Time Machine". Use the time line on the right to navigate to the previous back up of the library that you want to restore. (Likely it is in the Movies folder.) Click on your Movies folder in the sidebar. Click on the icon of the iMovie library that you want to restore. If you control-click on the library's icon you will get some options, including restore to another disk or place. Pick what option you want. Or, you can click the Restore tab at the bottom of the screen to restore it to your computer. If you restore the library to the same place it was on your computer hard drive, and the newer library version of it is still there, you will overwrite the new one.
You would lose any work done since your last back up.
Before restoring from Time Machine, you may find it easier to retrieve an earlier backup of your library from the iMovie Backups folder.
To get to the iMovie Backups folder, follow this file path from the Finder menu:
Go/Home/Library/Containers/com.apple.iMovieApp/Data/Library/Caches/iMovieBackups
NOTE: If running Ventura or later, in the above file path substitute iMovie for com.apple.iMovieApp. So, for Ventura or later, the file path would read:
Go/Home/Library/Containers/iMovie/Data/Library/Caches/iMovieBackups
When you get there you will see a list of previous backups of your iMovie library. Click on one dated that you want to recover. iMovie will open in that library. Navigate to your projects browser (where your projects are displayed as icons) and see if your projects are intact.
-- Rich