I agree that some kind of filter to determine whether or not the person is at least HG+ is probably in order.
Not sure how to (legally) do so, however.
Also not sure that what you're actually seeking there is a high achiever, either.
In fact, for a teacher who works with gifted students, I'd want someone who has experience with the darker side of being gifted. In other words, the IDEAL candidate is someone who has personally battled:
a) anxiety,
b) social problems related to giftedness,
c) underachievement, and
d) perfectionism.
Because only with that kind of background can a teacher truly help HG+ kids with some of their most common difficulties.
