Hi,
First, check your Applications folder to verify that the iMovie app is in fact deleted. Whether it was deleted or not, follow the below procedure to reinstall iMovie.
To update/redownload iMovie 10, drag your
iMovie 10 app from the Applications folder into the trash, but do not empty the
trash. (You can skip that step if you had iMovie 10 on your computer before,
but deleted it.) 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.
-- Rich