She has a crooked nose that she is said to have gotten from fighting with her fists as a girl.
Aeldene is not particularly strong in the One Power. Her level of strength is described by "The Wheel of Time Companion" as 27(15) which is a middle level in Aes Sedai hierarchy. With this level of strength she is unable to open alone a suitable gateway to Travel.
She is no more than middling strength in the One Power, yet Siuan must hold her tongue when Aeldene scolds her.
She took over as the head of the eyes-and-ears of the Blue Ajah when Siuan Sanche was raised to Amyrlin. One of the agents that reports to her is Duranda Tharne. Only two or three women among the Blue Ajah are meant to know her identity; Siuan herself was unaware of her replacement.
She arrives in Salidar and demands that Suian give back the eyes-and-ears network. She publicly upbraids Siuan, shouts at her and nearly starts a fight with her.
She also attempted to pump out the identities of those agents working in the Amyrlin Seat's network, but the other Ajahs did not want the Blue Ajah having access to both networks, so Siuan retained that knowledge.