[DanEC]

You can topcoat it with SEM semi-luster clear plastic and vinyl coating that is available in a spray can. The problem is that you can't clean the surface thoroughly before applying the coating for fear of removing the signature. This could result in peeling and lifting later if any Armoral or other treatments have been applied to the door. Careful cleaning of the door around the signature and then applying a couple very light coats of clear might work. But probably removing it and replacing it with another glovebox door as Rokfor suggested is the easiest approach if you want to preserve it.