Name: Glenna FitzGibbons (a.k.a. Mrs. Fitz)
Sibling: Mrs. Baxter
Occupation: Ran the household at Castle Leoch
We know that Mrs. Fitz had a sister whose son was named Tammas Baxter. We know that she also had a granddaughter named Laoghaire (pronounced "Leeree"). Murtagh is also some relation of her husband's.
Claire met Mrs. Fitz shortly after arriving at Castle Leoch in S01-E02 Episode Castle Leoch. She's scandalized by how little Claire is wearing, and makes a point of finding her some clothes that are "MORE". In fact, she dresses Claire quite well over the next few weeks.
Mrs. Fitz appreciates the fact that Claire is a healer, and can take on some of the "physicking", suggesting that if she does a good job, she will earn Colum's good will.
One funny scene in S01-E02 Episode Castle Leoch is when Mrs. Fitz is helping Claire get undressed for bathing, sees her bra and asks, "What kind of corset is that?" Claire answers, "A brassiere ... it's French ..."