Just keep asking for more speed. He will only be able to trot so fast before he breaks into a canter. There are ways of doing this, one of which is cracking the whip behind him. Another is clucking (or kissing) to get him to understand that you want forward movement. I use clucking in a general sense to mean speed up. I use words to denote what gate. Walk, trot, extend, canter ect. By clucking, I am only telling the horse that I want it to go faster or to move from a stop. (In western, clucks and kisses are often used to denote the gate. I use an english approach where clucking is used to increase the horse's speed.) And the last is to actually touch him with the whip to let him know you really mean business. I prefer to use the first two choices and then go to the last if I get no response. Eventually they learn that when you ask with verbal type cues that you mean it.
Now on the kissing or clucking and using that to mean to speed up.... there is a right way and a wrong way of doing it. Once a horse has learned that cluck=move, then you can use the cluck and time it to the position of the feet to help encourage the horse to move faster. It is all related to the timing and the hind feet. It is hard to explain in words, and easier in person. But it has to do with the horse's lead and where the hind leg is that impels the horse forward. I will try to make this clearer than mud! LOL...
The goal is to get the horse to spead up by clucking to make the feet move faster. So you cluck in time with the gait which drives the horse faster as the horse thinks "oh… she wants me to move a foot". In other words, the faster you want the horse to move, the faster your clucks will be. It is in time with the gait. The easiest way to do this is to watch the horse's hind feet. You would specifically watch the inside hind leg. When it is just ready to leave the ground, give the cluck. This causes the horse to want to move that leg further forward faster and results in increased speed. If you cluck when the horse is just putting that hind foot down, it will cause the horse to shorten it's gait and want to slow down. It takes some practice to time the clucks just right, but when you do, you will see what effect it has.
Unlike the previous two posts, I do think it is necessary to teach all horses to canter on a lunge line and in a cart. The reason is that while cantering the horse does use different muscles than trotting. I agree that for stamina one would use the majority of lunging activity at a trot, but by cantering some it helps to round out the look of the horse. And the primary reason for cantering in a cart is so that a horse learns what a cart's bouncing feels like should it ever spook while under harness. The last thing you want is a horse to spook and then get even more scared because it has never experienced the difference in the cart bouncing at the three beat gate of the canter. Besides, many of the combined driving events do require cantering on the course. And as a side note, I see my horses canter much more often at play than they do trotting... The reason goes back to what Sue_C said. The canter is a much easier gait which uses less energy than the trot does.
edited to fix spelling error.
