Yeah honestly I don't blame Nazuna for being jealous since Kyle is slacking alot on teaching her compared to the JK trio he only recently just met. Though I am surprised she merely chose to insert her into the training instead of anything destructive. I would give her props and say she's acting her age, but i still have my doubts that this is all we'll see of her jealousy.
Also it seems like a plan to cause discord has conveniently come in good timing, but like others have speculated, Kyle is probably going solo if he's allowed to.
In which case might be interesting to see considering if the trial will end up being a tag team tournament.