For more details, what operating system and iMovie version are you running?
Meanwhile, check your disk space by clicking on Apple Logo>About this Mac>Storage.
If you do in fact have sufficient disk space, try redownloading iMovie. That should solve it. To update/redownload iMovie 10, drag your iMovie 10 app from the Applications folder into the trash, but do not empty the trash. Sign in to the app store and open your purchases folder by clicking on your name at the bottom of the app store side bar. You will see your purchases displayed, including iMovie 10. Redownload/update iMovie from there. If not successful, drag your present iMovie app out of the trash (if you moved it there) and return it to the Applications folder. However, the download should be successful. After redownloading see if the "no disk space" is cured.
-- Rich