More often than not with new riders I see them not driving with their seat and this causes horses to break down. A horse can tell a confident rider, and the confident ones are the ones that can keep them going. My mare plays this game with the kids where they will try and get her to lope, only she'll just trot faster and faster. Then, in their inexperience, they will lose their seat and have to stop and regain it. She learned this.
Cue for the canter as you were taught on this horse and keep your outside leg on until he picks it up. Make sure you are moving your hips with his, rolling them an moving with him. New riders tend to brace and think too much about staying on. An experienced horse knows if an experienced rider poses resistance with their seat, it means slow down. This is called a half halt. They think that is what you want. Breathe, relax, think forward thoughts and makes sure you are moving with him and looking up at your next vantage point. Literally just thinking "canter" will help you.
Pssh.I didn't pick up the wrong lead
It's called a counter canter...
...A very advanced maneuver.