Have they had training to teach IELTS, or are they simply an English language teacher?
You need someone with extensive knowledge and experience with IELTS training specifically, not just English teaching.
Are they a native speaker?
Some non-native speakers can be good IELTS teachers, but you have to make sure that their English proficiency is very high. Ask to see their IELTS score. If they do not have a minimum of 8.5, they aren’t really qualified to teach you IELTS. Personally, I’d prefer to see a 9.
Do they understand how the test is scored, and can they explain it to you so that you can understand?
It is no secret — there is a sample of band score descriptors made available to the public by IELTS. If your teacher doesn’t know about these or is unable to explain them in relation to your work, then they are not qualified to teach you IELTS.
Have they ever been an IELTS examiner?
In my experience, IELTS examiners and ex-IELTS examiners make the best IELTS teachers but they aren’t really supposed to disclose that information.