Trail horses go along by pulling themselves along from the front. It is completely different to a horse that pushes from behind.
For an analogy jog along by shuffling, then change it to jogging and lifting your knees to your shoulders.
You will be asking the horse to go completely differently. He does not have the muscle, he does not have the stamina. It will be painful physically. You must never overface him mentally.
The fact that he was a lesson horse may be a plus, as he might already have some understanding.
A horse who goes along with a higher head and no contact does so because of bad hands. They are trying to stop the hurt. The horse being ridden with bad hands will either do that or will do the opposite and put their head down to lean. It stops the bit hurting the mouth as much.
As you are asking this question you are not a horse trainer who knows how to fix this problem,
However to become a horse trainer what you do is take a quiet older horse like this and take lessons and learn how to train this horse.
Rinse and repeat with older horses who need your help with different problems. That is how you get the skills to train horses. Thipen as your skills increase you can start with retraining younger horses. Then finally you can train your own young horse. How easy it is with all that experience behind you and the great instructor still helping you.
Good luck on your journey.
The first thing to find out with a horse like that is if it will still be sound with the increased work. Some are okay dwardling and not up to the physical change.
The most important thing to learn is that you need to listen to the horse. You will learn from each horse. Do so with a great instructor and you will go far.