Do I need to tell SLT that I'm applying elsewhere?

[DorothyL]

Or can I wait if I get an interview first?

I would always ask when putting in an application, because you will need to put your current head as a referee, and it is polite to ask first!

Also, references are taken for every one called for interview, so they may find out before you tell them.

Well, you certainly need to tell your referees, and one of them should be your current headteacher wherever possible, so yes - you need to tell him / her at the very least. It's not unusual for references to be taken up before interview.