When you say that adding the transition "does not work" what procedure are you using to add the transition and what are you observing when you try? Do you get a pop-up message that states that there is insufficient media? Do transitions work when you add them between photos? Have you clicked on the Settings button above and to the right of the timeline and unchecked the box that says "Automatic Content"? Does a 1 second transition work, or does the problem happen only with longer duration transitions?
Transitions between video clips overlap onto what is called "residual media". Residual Media is the invisible portion of a video clip that remains when you trim back a clip. It only applies to video clips, not photos. A certain amount of residual media exists by default in an untrimmed clip, so that transitions of 1 second can be added. However, transitions of longer than 1 second need more residual media than the default amount. If you try to add a 4 second transition you will get a pop up message that there is insufficient media. In that case, you need to trim back the video clips on each side of the transition to create more residual media. Or, as léonie suggests, add a still frame of the last frame on each side of the transition.
If the problem still persists, try deleting 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.
-- Rich