I was a TA for many years, and teachers and support staff should always try to give ALL children a fair 'go' at all activities, even ones they may not be particularly good at. But it is often the quieter, well behaved child who merges into the background, who gets overlooked.
If you have a friendly TA or helper in the class, maybe you could ask them to help.
In my ten years as TA I ran recorder groups, did computer activities and touch typing as lunchtime clubs. I coached children to play percussion to accompany the Christmas production each year, and for a while ran a percussion club.
I guess the most obvious out-of-school activities are sports, music, and drama. There are also groups like Brownies (or whatever the modern equivalent it is), and similar organisations. When I did voluntary family support, with children who were having difficulties at school, we had a 'drop-in' room so children could get out of the playground, and do activities, or just chat to an independent adult, who wasn't 'staff'. A Yr6 girl, who had some behaviour issues in class, surprised me when she told me she was a St John's Ambulance cadet, and she was proud of the medical knowledge and skills she was acquiring.
So there is plenty going on, out there, and I hope DD finds something suitable.