My DD9 is a major PITA to everyone in the family (me, DH, DD18 and DD16). She always has to be doing something and bugs the rest of us endlessly. She also can get frustrated if she doesn't understand something immediately. She is better with her older sisters explaining the homework than me. Perhaps another kid explaining (if one is available) would be better than Mom or Dad.
I don't even know if she is gifted. She doesn't have the sensory issues, though DD16 did at age six. We got tired of it and told her she was too old to do that stuff (clothing, food texture, etc.). She still has some issues but she hides them from others because that is what is socially acceptable. I know others might not like that technique, but she now outwardly appears normal in that respect.
I am open to all suggestions. My older two were not like this at age nine - they could entertain themselves. Perhaps being close in age helped. The problem with physical activities is if she doesn't get it immediately - riding a bike, hitting a ball, etc. - she quits. She will be doing just fine in a physical activity/sport for a few months, then faces some sort of "failure" and quits. We've made her continue to a logical stopping point (e.g. earning a belt in karate), but we have trouble having her stick with anything. Never even went to the next karate class to receive her belt after she passed the test - she didn't even care. Middle kid has some perfectionist issues with sports, but not to the degree that she expects she will never strike out, never make an error, etc. While the older two were sometimes balking at going to practice or a game, they would go (and were happy once they got there). Youngest will yell, scream, cry that she doesn't want to go, will not get dressed in her uniform, and sometimes locks herself in a room. We have had punishments, but doesn't seem to work. I sympathize with your situation.