I have been leasing various horses for the last 10 years and it is always a frustration that when I spend time and energy and money on lessons putting some training int the horse, then the next person that rides him could care less how he moves as long as he canters up the hill. However, for me I always look at it as it's training for me to learn how to train a horse. Gives ME added value as a rider and leasor.
However, I think you can find better than that horse. I have leased 6 different horses over these years and I have found some real winners!
Just don't take the first thing that comes along.