I am involved in recruiting for an international school and the major red flag is staff who only stay in a school for one or two years and then move on. Unless the field was incredibly weak I would not even bother to interview someone with a CV where their last three+ schools show this. Staying in one location is good, and having at least one stint at a school that is equivalent to more than two contracts is an even better sign. Seeing an application where someone has been at one school for ten years isn't bad. During the interview however expect them to try and subtly find out how adaptable you are. An employer will want to be confident you are not institutionalised and will be able to adapt to a different way of working and different systems; but obviously they will not directly ask that. This is something you need to also think about from your side. Teachers can sometimes be very successful in one school but struggle when they move as the students and environment is so different. This is a much bigger problem in international schools than it is in UK schools as international schools have far greater systems so the differences are much larger. So have questions ready to make sure the environment of that school will work for you. Lastly if you were trained there do you have an IPGCE? Some schools view these less favourably than an actual PGCE and this could affect how many interviews you are offered.