Your intial post said you were looking for a dressage trainer, then a later post said jumping. Which is it - or is it both?
A GOOD dressage trainer will train both you and your horse and make the (eventual) jumping better for both of you, so if the answer is both then looking for a dressage trainer who has shown OR had student that have shown SUCCESSFULLY (60% or above in RECOGNIZED shows) at second level or above. Even if you do NOT compete in either discipline there are MANY trainers out there who will give you the wrong/incorrect information. They'll probably believe it is correct but if they and/or their students are not doing well at recognized shows then you know the information they teach is most likely NOT correct.
If you can't find that look for an Eventing trainer (they do both dressage and jumping, with preferences USUALLY in the jumping realm). I'm not certain of the eventing levels but at least Training level with jumps around 3'3". Again with successful competition experience for themselves and students.
Before you select a trainer write up some questions and ask them, recording their answers. Then ask to watch both beginner and more advanced student lessons. By then you should be able to decide if #1 - you like their teaching style (some people need yellers, others don't care for them), #2 if you think instructor knows what they're doing and #3 if your eye finds how their students are riding "nice" (means they're probably performing correctly versus yanking horses around, etc.).
Other things to ask:
1. Can they/ will they get on your horse if you and horse have an issue? They have been a few times over the years that what appears to be happening (to the instructor) is not at all what it feels like. In that case I ask the instructor if they can get on - then they can do what they've been telling me to do. Most times they figure out something completely different than they thought is the issue - then they work with horse on that and have me get on, as soon as they get off after working the issue, so I can "feel" the correction.
2. Do they have any lesson horses so while you're trying to learn you can first feel the "correct" way the horse is to move (before attempting to teach it to the horse). That shortens your learning time, and the horses too!
Dressage is for Trainers!