She was described as having long hair streaked with gray as well as a square face.
In "The Wheel of Time Companion" her level of strength is described as 19(7) which is a bit low considering the rank and role assumed by Tamra in the main books. Most probably her real level is around 17(5) which can be also considered the minimum level to become an Amyrlin Seat.
She was thought to be fair and always just. She also seemed to be a devious manipulator.
She was Noane Masadim's successor and Sierin Vayu's predecessor. This makes her the first known Amyrlin Seat to be raised from the same Ajah as her predecessor. It has been speculated that as with the case of Marith Jaen and Siuan Sanche, this consecutive pair of Blue Amyrlins was the work of the political skill of the Blue Ajah First Selector of the time, Eadyth, who was also a Sitter at the time.
On the last day of the Aiel War, as the Battle of the Shining Walls ended, Tamra was one of three people to hear Gitara Moroso's Foretelling of the rebirth of the Dragon immediately before Gitara died. At this point Tamra began her search for the child she knew must be born by appointing searchers. The other two present, the then Accepted Moiraine Damodred and Siuan Sanche, were forbidden to reveal this secret to anyone. 
When the Black Ajah discovered what had happened, they—Galina Casban and Chesmal Emry in particular—tortured and murdered Tamra, along with the Aes Sedai that she had sent searching for the Dragon Reborn. Tamra's death in the tower was explained by an announcement that she had "died in her sleep." This left only Moiraine and Siuan outside of the Black who knew of the rebirth, so this began their search.