Cairlyn is not particularly strong in the One Power. Her level of strength is described by "The Wheel of Time Companion" as 22(10) which is a middle/high level in Aes Sedai hierarchy. This level of strength can be just enough to open alone a suitable gateway to Travel.
She has remained loyal to the White Tower during the split.
Cairlyn was one of the captured Aes Sedai to be interrogated by Verin Mathwin in order to discover the White Tower's intentions towards Rand al'Thor. In reality Verin used her mild Compulsion to implant in their minds some instructions about Rand.
Particularity of this characterEdit
Cairlyn Nesolle is described only in "The Wheel of Time Companion", she is never mentioned in the main books of the Wheel of Time. If we have to took as good the informations from the Companion, she is the only Yellow mentioned in the party sent to kidnap Rand in Cairhien.
But this is in contradiction to the description of this group in the main Books, because we know well the number of sisters and the Ajah involved in the kidnapping group and no Yellow sisters were ever counted in that party.