The question is often asked and some of us are surprised at the quality (or lack of quality) of some teachers. But here is one way to help pick a teacher.

Listen to recordings of known good professional horn players. (buy them, borrow them, check them out from the library,check you tube). Learn what you are supposed to sound like. Then find some teachers and make an appointment to meet with them. Part of that appointment should be to ask them to play something "to demonstrate" what they think you should sound like (or for parents what the student should sound like). If that sound doesn't match what you've been hearing then move on to the next teacher applicant.

I think a good teacher should be able to produce a nice clear good tone. I actually think a teacher should be able to produce a good sound and bad sounds on command. An example is I might play a section of a piece and say here is what many beginers might sound like and then play it again showing what I get them to play like. A teacher who can play good and bad shows they know what makes a bad sound and what it takes to make a good sound.