iMovie

Try resetting your iMovie preferences and see if that cures it. To delete/reset preferences open iMovie while holding down the Option and Command keys and select to delete preferences in the box that appears. iMovie will open in a new library. Reopen your old library to get back to your projects.  Deleting preferences is a safe procedure that will not cause data loss or disruption to your project.

If the above doesn't cure it, try these diagnostic procedures:

Opening iMovie in a new library

Try opening iMovie in a new library. To do that, open iMovie while holding down the Option key and then selecting to create a new library in the box that appears. Opening iMovie in a new user account Create a new user account from System Preferences/Users and Groups and try to open and use iMovie in the new account. You can use the Guest account on your Mac for this purpose.

Safe Mode

You could also try booting up in Safe Mode (see Finder menu for instructions) and, after everything loads, immediately shut down and reboot in normal mode. Then see if iMovie will open when you are in normal mode. (It won't open in Safe Mode.)

New User Account

Try opening iMovie in a new user account. You can use the Guest account on your Mac for this purpose.

Updating iMovie

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 and return it to the Applications folder.

Resetting the System Management Controller

Try resetting the System Management Controller (but no longer available for the new M1 computers):

How to reset the SMC of your Mac - Apple Support

Resetting the NVRAM or PRAM

Try resetting the NVRAM or PRAM, although this issue would be fairly rare:

Reset NVRAM or PRAM on your Mac - Apple Support

Contact Apple Support

If none of the above resolve your issue, contact Apple Support. The techs there have the capability of remotely accessing your computer that we cannot do here. To contact apple support click on the Get Support item in the upper right hand corner of this forum’s screen. Navigate to a place where you can enter your phone number.

-- Rich