I'm doing my first event of the season next weekend, and it is also my first event since the rule change about carrying a whip during your test..
When riding at home, I always carry my whip to the inside and switch it over when I make a change of direction. Since I've never carried a whip during a test at an event, I don't have experience with the protocol for that. Is it okay to switch your whip over to the inside when you change rein? Or should it stay to one side for the entirety of the test?
I usually don't do this (it is much better to leave it on the side of the horse that does freaky things: i.e. falls in, doesn't bend correctly, etc), but if you have to change the whip, then just flip it over the horse and grab it by the handle. In other words, act like the whip is a clock hand and rotate the whip over the horse. This is typically much easier unless your horse is super spooky.
My dressage instructor, who is also a judge says it's okay to switch sides if you need it, but only if you can hold reins in one hand (the hand the whip is starting in) and keep contact with the horse's mouth, while reaching over with the free hand to take the whip.... I generally just leave it in my left hand since that's where we are weaker.