Teire is not very strong in the One Power. Her level of strength is described by "The Wheel of Time Companion" as 32(20) which is a middle/low level in Aes Sedai hierarchy. With this level of strength she is unable to open alone a suitable gateway to Travel.
Teire was part of Elaida do Avriny a'Roihan's secret expedition to kidnap Rand al'Thor in Cairhien. After kidnapping Rand and escaping capture during the Battle of Dumai's Wells she flees to Dorlan along other sisters.
Particularity of this characterEdit
Teire Alentaine 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 third Gray mentioned in the party sent to kidnap Rand in Cairhien.
But this is in contradiction to the description given by Galina about this group in Lord of Chaos. There, we know the number of sisters involved and the Ajahs involved in this kidnapping group, and no more Gray sisters than one (Coiren) were ever counted in that party.