Yes, you can move an iMovie Library back and forth between drives. First make sure that the external drive is formatted Mac OS Extended (Journaled). If the external drive is not already formatted Mac OS Extended (Journaled) you can reformat it using the disk utility app on your Mac. Reformatting will erase all data on the drive, so make sure that you have backed up or moved elsewhere anything that you want to keep.
Then do a copy and paste of your iMovie Library from the Movies folder to your external drive. Make sure that the library is working O.K. on the external drive, and then you can delete the one on your computer's drive.
For safety's sake, it's a good idea to keep a Time Machine backup, or other backup, of your iMovie Library. Libraries can get corrupted, disks can fail, and if you don't have a backup you could lose all of your projects.
-- Rich