You need to have someone else move first I believe. The last villager who recently moved in won't move until someone else does.
This has been mostly true in my experience too, but from what I hear it's possible to get the most recent move-in to leave if you simply never speak to them at all.
Though if that fails I've got a couple others I want to move out too, so there's that.
Definitely making any buyers clear their voids first though.
