Do you mean a canter or a gallop? Cause I wouldnt gallop my tb mare in any inclosed area, like a round pen or arena. I usually take her to open fields. But when just starting out and galloping for the first time its easy to go up big hills, cause you can just get right into jumping position and hang on and let your horse do all the work, while you steer.
Also I would be carefull when galloping a horse for the first time, make sure you do lots of transitions from the walk to trot, trot to walk, trot to canter..ect. Because you don't want your horse to get the idea that that's all your going to do in an open fields is go! Cause your horse might take off the next time you get into an open area.
From east to west a travlin gypsy found her prancing pony for now their hearts run as one...into the north