What all have you tried to get him to trot?
If you are leading him speed up and see if he'll trot along beside you. If not you have a few options that are known to work.
1. While leading him carry a dressage whip in the opposite hand. When you proceed to speed up and he doesn't quickly tap him on the hocks with the whip while telling him to 'trot on'. He should start to trot, and when he does reward him for it. If he does not try again with a harder tap, progressively get a bit harder until he trots. While many horses will respond to this not all will.
2. Round pen work, I don't suggest this for a yearling in most cases, but 10 to 15 minutes shouldn't hurt him in any way. You can choose to free lunge or use a lunge line, either way should work, but you'll have more control with the line. Ask him to walk and once he's warmed up and going well ask him to trot, if he does not slap the ground with a lunge whip and he should move forward. Once he does reward him. Continue to work on this and since you are using verbal cues remember to say ' trot on!' or ' Trrott!' when you ask for the trot. He should get the idea.
3. Long lining. (Some people call this ground driving.)If you do not know how to do this I would ask for a professional's help as you and the yearling could get hurt. The mini would be put in a surcingle and either a halter or bridle (preferred) with two long lines attached. The mini would be taught to move forward as if he were being driven.
Those are the three most common methods I've used, though I've rarely had trouble with a yearling during leading and gait changes, it always seems to be the seniors that decide to have some fun with me, LOL.
"They see me rollin, They hatin, Patrolling they tryin to catch me ridin dirty"