Elaiva 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.
Later it is reported by Sorilea that all the Aes Sedai prisoners have sworn fealty to Rand.
As with many Aes Sedai sworn to Rand, Elaiva probably fought the Last Battle on the slopes of Thakan'dar. It is not stated whether she survived or not.
Elaiva Walfor is described only in The Wheel of Time Companion, she is never mentioned in the main books of The Wheel of Time. Taking inference from the Companion, she is the second Gray mentioned in the party sent to kidnap Rand in Cairhien.
But this is in contradiction to the description of this group in the main series, because we know well the number of sisters and the Ajah involved in the kidnapping group and no more Gray sisters than one (Coiren) were ever counted in that party.