Was the old version of iMovie by any chance an earlier version of iMovie 10? If so, even though you deleted it you can update it to the most current version of iMovie 10 that your current High Sierra operating system can run. Otherwise you will not be able to get iMovie 10 unless you can upgrade to at least Mojave 10.14.6.
In the event that you fall into the category of previously owned iMovie 10 version, here's the way to update it:
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