Someone who is observant and can understand you and your horse, who can push you and keep things fun and interesting
Someone who knows your limits but will push you to make you better and someone who really knows what's best for
That they push you past your comfort zone, are honest and you're able to communicate well. As well as then understanding your riding style. Good horsemanship and being very sensible. A clean and well kept barn. Safe and reliable school horses. Someone that will tell you what they're thinking. That they teach you in a way that you understand.... good luck !
The best think to look in a trainer is that you guys click and you feel comfortable with that person. Also you need a trainer that goes with your price range!