DD cycles in the summer (a racing club) but she needs a lot of physical activity to burn off energy. She wants to learn to ride but all three of the possible BHS approved stables near us have waiting lists (which she's on).
In theory she goes to a dry ski slope every other week and we could up that, or go to the indoor snow centre for proper lessons.
She's missed the boat with gymnastics and football, we fear, she's been to both in primary school but stuck with cycling much longer. She also gave up on karate so I fear any marital arts would be a hard sell.
She went up to about stage 4 in swimming and then did some rookie life-saving but she's got quite fed up of that due to not moving up to the next stage. They suggested some private lessons to move up quicker but she struggles with having too much attention just on her so says she doesn't want to do that.
So far I've thought of:
Skiing as above
Climbing
Rugby (she's quite small for her age though).
Trampolining if you can start at her age?
Cricket but she's declined before and it's another summer sport.
We don't have many unusual sports in our area as we are fairly rural.