I dislike schooling prefer hacking, much more fun
I do find tho to help get a horse more forward going and off the leg is to do lots of transitions. Direct transitions to start with and then some indirect once they're more forward going in the direct transitions.
Plenty changes of rein, circles (you can start on a larger circle and gradually make it smaller and then bigger again), serpentines, figures of 8 also try some lateral movements (turn on the forehand and leg yielding are easier 1st movements to try)
Pole work, the obvious trotting poles, but you can also try making paths (almost 's' shaped to make it a bit more difficult) and trying to get the horse to walk and trot through without going over the poles, also rein back into them.