This is a hard one - We've had it before at our gym too. The coach of this particular gymnast went to the chemist and bought some of those small deodorants and, without making a big deal of anything just gave them out to every member of her group. She said something like 'Oh, These were being given out free in town so I thought I'd get one for everyone!' hehe its a bit sneaky, but it worked! Our particular gymnast had only just turned 10 though so I doubt she had realised or started wearing deodorant at that stage!
It is much harder when the gymnast is younger - I had a gymnast who was only 7 but had really bad B.O. In the end I asked her mum if she had any other leotards as with her doing 4 days of gym a week it was probably difficult washing and getting 1 leotard dry before the next session. It turned out she did only have 1 leotard and it was only being washed once a week!
In your situation, I'd say speak to her coach and see what they say. It is better that the gymnast is told though, rather than potentially having people talk about her behind her back.
I have a friend, also a coach, who will bring up conversations which lead around to a difficult topic. For example; if someone is a bit smelly, she will bring up a conversation about deodorant! haha again, it sounds silly, but you might find out the reason why the person smells!