To train a horse to extend his trot, ask the horse to extend the stride length by increasing leg pressure. If a horse breaks into a canter, simply ask the horse again to extend the trot with advice from an equestrian team head coach in this video on horse training.
To train your horse to extend his trot you first need to make sure that your horse is able to carry a nice regular working trot. And to begin with we'll stay at a rising trot. Once you're comfortable with a nice working trot, to ask the horse to extend, I'm going to increase my leg pressure and often when we're first teaching our horse to extend, it will break into a canter because they don't understand the question and I'm simply going to ask again. This time she lengthened her stride rather than breaking into a canter. It's great to practice lengthening and collecting the stride as it increases your flexibility with your horse and the responsiveness to your aids.
Specialty: Hunter, Jumper, Equitation