Hi,
You should be able to move clips around the timeline by putting your cursor on them and, while pressing down, dragging the clip to another location in the timeline. If you are doing that and it is not working for you, try the following diagnostic procedures:
Try opening iMovie while holding down the Option and Command keys and selecting to delete preferences in the box that appears. iMovie will open in a new library. Return to your old library to get back to your projects. Now see if your can move your clips in the timeline.
If no luck, try creating a new project and see if the issue is resolved there.
If still no luck, as a final resort do a redownload of iMovie. To do that drag your iMovie app from the Applications folder to the trash, but don't empty the trash. Then sign in to the app store and open your account by clicking on your name at the bottom of the app store side bar. You will then see a list of your purchases. iMovie should be one of them. You can download it from there. If for some reason the redownload is unavailable or unsuccessful, drag your old iMovie app out of the trash and replace it in the Applications folder.
-- Rich