Does she always gallop off at the same gate/ place? Maybe something could be spooking her. One time my shirt just was ruffled by the wind and my horse totally freaked out. So look around that area to see if there is anything that's flapping or making sudden movements.
She might also have a bad memory of that gate. Did she every get hurt around it or from it? Or maybe she got spooked badly once, and never forgot it. Horses are known to have fears like that.
Make sure to always be very calm around the gate. If you tense up, she will too. If possible, could you take pictures of the gate area? There could be a number of things that would spook her/she is scared of.
She could also dislike something you do when you groom her. It could be her body has sores that are not noticeable, or the tools are uncomfortable for her. If you let her run off then feed her without grooming her, she thinks she can take advantage of you.
Has anyone else ever tried to lead her out? If not, try to get a strong adult to lead her out.
I would also advise using a stud chain. I use them when I am dealing with stronger, bigger horses that try to pull away.
Also, just try to go sort of close to the gate. Not where she gallops off, but farther back. Stay calm, pet her, and talk to her soothingly. Once you feel her relax, make her take a few steps forward. If she tenses up, get right on back to petting her. You can even offer small treats. Once you finally arrive at the gate and you know she is about to gallop off, gently pull her forward and pet her. Offer a treat in gate.
Hopefully this helps.
No hour of life is wasted that is spent [in the saddle].