Nelavaire is not particularly strong in the One Power. Her level of strength is described by "The Wheel of Time Companion" as 28(16) 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.
"The Wheel of Time Companion" confirms her Cairhienin origin.
She remained loyal to the White Tower during the split following Siuan Sanche's deposing. She is one of the sisters who was captured after the Battle of Dumai's Wells. She has now bonded the Asha'man Naeff.