Hildr is a female Greybeard follower, and yes, she too has a beard.

She can be found in High Hrothgar with the others. Her combat style is the same as the other Greybeards, so she'll use shouts and fists to fight. She is marked as Essential like the others, so she won't die. Hildr is also silent because the power of her voice is too strong for mortals.