A Good Trainer
A lot of the applications from a good instructor apply to a good trainer as well but here are a couple more.
Loves, respects and is patient with the horse - They keep a two-way conversation with the horse, and they care about the horse’s state of mind. Knowing how to read horse language will help to determine when to push for more, and when to leave it alone. This is paramount.
Has a deep and wide tool chest - This can only come from years and miles in the saddle. The trainer must keep an open-mind and understand good ideas for training can come from a variety of places - Everything from studying the horse in nature to looking at other riding disciplines outside their own.
Must be effective - Most horses train relatively easily if they are in the right program. The horse is looking for a leader and they can spot a fake. Make sure your trainer has a good work ethic. They should show up and be 100% present when working with your horse. Although there will be bumps along the way, your horse should show improvement weekly. Discuss the goals with your trainer and make sure they stay in constant communication about your horse’s progress.