Don't forget to add that a Hand Gallop is a gait where the horse works off of their hind end, without allowing your horse to go flat and heavy on the forehand.
Hand Gallop, you also want to get up off of your horses back to free the back. A Hand Gallop is not a seated gait, it is where the rider is up in a functional two point position.
You see Eventers doing a Hand Gallop between fences.
Here is a video of my horse and I out on CC, and you can see a Hand Gallop: