Think of riding your horse’s outside hind leg actively through the turns to your jumps, to keep that canter well engaged behind. The outside hind leg is the beginning of each canter stride. Engage that hind leg, and you will engage the entire hindquarters.
The fastest cross-country horses are not necessarily the fastest horses in general, but the ones that are the easiest to set up for the jumps. So work on your horse's adjustability.
Every well ridden corner is a suppling exercise, and should be recognized as such.
A tip for all of the instructors out there... When a student has a lightbulb moment during a riding lesson, ask them to explain it you in their own words. This way it becomes even more cemented in their own mind, and you can more easily help them find it
Always think about the depth of the water when deciding how fast to approach and negotiate a water obstacle. Riding too fast in deep water can easily cause the horse to lose his balance or even fall.