In my experience, most admins completely understand that a percentage of their teachers will move on every year. Unless yours are completely toxic they're not going to non-renew you just because you're looking.

I've been shopping around for a couple of years. Every application I've filled out asks for references, and most send an auto email to them as soon as you submit the application. Not including your current admin as a reference is a red flag to some. Anyone who's halfway serious about you is likely to call your campus principal, even if they're not included on your references. You can't hide the fact that you're looking, at least not for long.

My advice - let your admin know you're considering other opportunities, submit those applications, see where it goes. Unless you've already signed a contract elsewhere, sign your renewal when it comes out. You have until 45 days before the first day of school to resign without penalty. For most districts that's roughly the 4th of July.

Unless your admin are just complete turds, in that case tread lightly I guess.