A similar entry appears in the Wheel of Time Companion confirming the information available in the main story arc.
Author: Atarah al'Norahn
Anvaere is one of Moiraine Damodred's older sisters, making her a high-ranking Cairhienin noblewoman. She has one other sister, Innloine.
According to Moiraine, Anvaere doesn't care for anything except for horses and hawking. She also has a bad temper.
When Jarna Malari asks Moiraine if either of her sisters has a chance of claiming the Sun Throne after Laman is killed, Moiraine replies that that both of her sisters are well thought of, but not for the throne. She adds silently to herself that no one would trust Anvaere's temper on the throne. Moiraine says that no one will support Anvaere for the throne, even within House Damodred.
(Reference: New Spring, Chapter 6)