In five years of having chickens, I have never once heard a chicken cough. It's not a good thing. You should keep her separated. This is a hard subject for me because, like most old time chicken keepers and breeders, I don't believe in treating respiratory illness. What may have happened is that the younger girls were carriers of something and your older hen caught it from the new ones, but it's really hard to say and no one can reliably diagnose anything over the net. Watch her, give supportive care like extra protein, organic unfiltered Apple Cider Vinegar with "the mother" (sediment) in her water, just a little. It has healthful benefits and vitamins. Then, observe her over a several day period. If she doesn't get better, you'll have to decide to euthanize her or try a shot-in-the-dark treatment of antibiotics, though if she has a virus, that will do nothing for her. I have a no-treat policy for stuff like that, if it should ever come up, but I realize that is super hard for most folks (it is for me, too).
Hopefully, it's just something that got stuck in her throat and she'll work it out.