It's a fact that when you remove a tooth and do nothing, the other teeth will move and go out of alignment. Dentists call this "your bite." When your teeth go out of alignment and your "bite is off," all sorts of things can happen. You can get headaches, pain, infections.
I'd have an implant installed or at least a "flipper" if it's a front tooth. You can also get a single unit bridge made if it's a rear tooth. You need to fill-up that space before the teeth move around.