I could argue the case for both approaches. I don't see a problem with deciding to advertise (because you'll get applications from people who wouldn't be interested in a fixed term role, so a better choice of applicants) or to offer the post internally in the first instance (inevitably ending up with the person in post) if they have proved to be excellent. What is important is to be open with the person about the process that the school will follow - because otherwise you'll lose them whether they are good or not, because they won't feel that you (they) are being treated fairly.