Her name indicates that probably she was from Tarabon. Tesien was born in 692 NE and went to the Tower in 705 NE. After five years as novice and four as Accepted she was raised to the shawl in the year 714 NE. Her level of strength was 15(3).
In TWoTC it is stated that the Highest before Galina was also of the Black and that she was killed by Ishamael for her involvement in "The Vileness" because she was part of the Black Ajah Supreme Council. It is not know if Tesien is this Highest or the former one, but the dating of her lifespan indicates that most probably she is the same person.