Medium trot?

Make sure you have completely established a good, rhythmical working trot and that horsey is going forwards nicely, pushing from behind, coming thru his back into a nice even contact. Rhythm is really important here, down the long side, keep the rhythm, don't increase the speed, but ask your horse to lengthen his stride, half halting before the corner to bring him back to working. Try not to pull, use your seat and voice. It will take a while before they get it, although some are much quicker at getting it than others. Make sure horse is really forward and straight. Best of all - get a good trainer to help you.
 
General schooling to increase the impulsion. Lots of transitions, 15m and 10m circles. Build up the impulsion until he feels like a coiled spring then ask him to stretch out a bit down the long side of the arena, give him a fraction extra rein to do it if necessary. Be happy with just a few slightly lengthened strides to start with. Use transitions within the pace, working trot to lengthened strides and back to working trot again. Those lengthened strides will become a decent medium trot in time.

Once your horse has a bit of an idea what you want, pole work can help. Set up a line of about 6 or 7 trotting poles on the centre line of the arena at normal distance for working trot. Ride up the centre of them as normal. If you now ride them on a diagonal line (so you're not aiming for the centre of each pole, but on a line running from eg the far left of the first pole to the far right of the last pole) , the distance between the poles is greater and the horse will need to lengthen his trot to avoid tripping up. Ask for the lengthening a few strides before you get to the poles and after a few goes the horse should get the idea of what you want. Your horse can tell what's coming based on whether you approach the centre of the poles or on the diagonal line. Gradually as improvement is made you can ask for more and more lengthened strides before the poles and ask him to keep it up for longer afterwards, eventually dispensing with the poles altogether.

Another useful way if you don't have an arena is to find a big hill and canter towards then up it a few times so the horse knows what's coming and gets excited. Then ask for the increased power as you approach the hill but don't give canter aids and if the horse goes to canter ask him not to. Usually they work it out for themselves how to lengthen, because they really want to go but you won't let them go up a pace. Just praise the horse lots when he gets it right. Test it by asking for the lengthening as you approach the hill, then returning to working trot for a few strides then asking for the lengthening again. It will soon become an established cue that gets you the same result on the flat whenever you ask but without the hill there for encouragement. Using the hill to start with helps the horse keep his balance in the lengthened strides and not drop onto the forehand.
 
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