Im not an expert but you could start seeing what he knows yourself by going into the school carrying a long schooling whip and asking him to walk on as you lead him (from next to his shoulder so youre not dragging him the way we normally might, so he knows this is different).
Say ‘walk on’ loudly, click tongue once and if he then doesn’t step forward within a second, gently flick the end of the whip towards his bum (you dont turn to do this you just use the hand furthest away from him to flick the long whip behind your back towards his bum.
The theory being ‘if I don’t listen to instruction I get a flick’.
Start gentle til he gets the hang of it. Walk for say one minute round the school. Practice Whoah command to stop. Pat him for being good each time so he knows he’s doing what you want.
Then Walk On and tongue click again, and if he doesn't walk, one gentle whip again. Repeat multiple times. This is work not fun. Change direction across the school occasionally. You lead him from the inside. So when you change direction you swap hands over. You could stop to do this. Practice whoah command then.
You shouldn’t be dragging him forward at any time. He has to listen to your voice and do what you say and do (ss Youll do the same walk or trot beside him) when you tell him, or he gets a sting wirh the whip. Just one. Start gentle but you can make it a proper sting if he is taking the piss and that will sharpen him up that you have expectations that he pays attention and obeys voice commands. .
Once hes got the hang of it move on to trot and jog beside him. The command being Trot On, click, one whip if he doesn’t. Continue as before. Go from walk to trot and back, practicing a stop now and again. Remember to praise him.
A tongue click only used to go faster and same with the whip. No tongue click or whip if he takes a while to slow down. Whoooooah in a low deep voice. A high pitched is used on going faster commands. Easy to differentiate if he doesn’t recognise the words.
The reason I’m saying do this from the ground is because we don’t know if he understands commands at all so it’s the best way to teach him if he’s forgotten them and you can see how he moves with no saddle or rider.
You can do the exact same thing on a lunge or riding him ie Ask for what you want, click tongue if it involves going faster, whip once behind the leg with a long whip (long schooling whip so you don’t remove your hand from the rein - but dont jab him in the mouth) etc.
Once you know he knows the commands on the ground he needs to obey them when ridden. He will then start to notice that when you say trot on you squeeze both legs and will soon associate that with squeeze-means-faster and will obey that so you don’t always need the voice command in the distant future once Hes Got It and is behaving!
Dont work him too long or he will get bored. Handful of pony nuts and a good pat at the end if the session for trying.