The truth must out
I am considering moving to another job, but don't know how to approach it with my current school. I've seen a job advertised in the independent sector, and as I have always worked in state schools (eight years), I could be seen as "selling out". If I don't get the job I'm worried that career prospects in my present school will be frozen. Do I ask for testimonials from my head of department and head before applying? Do I discuss that I'm looking around?
Be open with your employer. If you have given eight years' service, they can't be surprised that you are looking to move on to further your career.
You don't say how long you have been at this school. If you have a good relationship with the head, talk the issue of your career through, and ask for advice. If you don't get on, you are going to leave anyway. The job you want is in the independent sector. You might not be shortlisted, so why tell the head any more than that you are looking for a new job? Your current head will have to be a referee. I don't think testimonials are worth much as everyone knows that nobody says anything bad in an open document, even if the tributes make you feel better. It may be helpful if you find someone outside school to act as a referee, who could give a wider view on your abilities, such as a local authority officer or someone who has run a continuing professional development activity you have taken part in recently.