It is always a good idea, and safest, to quarantine any new bird(s) to your flock for 30 days. The stress of a new home can bring out hidden illness and it's best to know before you spread it to your flock.
I would check her over very carefully for lice/mites. She also could be like this due to feather picking by whatever other birds she was previously with. Also looks like some of it could be rooster damage also, the area on the back in front of the tail, and the bare spot behind the comb are common for rooster damage. I would feed her a grower feed with a higher protein content for a while, offering oyster shell free choice all the time. Do you know if she is laying? Hard to tell in a picture, and the feather loss likely makes it look worse, but she may have ascites, which is an accumulation of fluid in the abdomen which can be caused by reproductive problems, infection, cancers, or organ failure. Check the abdomen to see if it feels normal, or particularly hard, or water balloon like. You can compare with your other chickens for reference. If she seems ok then I would keep her separated and on a good diet for a while and give her a chance to recover. I'd also keep an eye on her droppings for any other signs of illness or internal parasites. If you have a vet that will do a fecal float test for internal parasites I would do that.
