Tili Qua was a female Jedi Master of the Chadra-Fan species (for more on female representation). She held a position on the Jedi High Council within the Hidden Temple. This occurred after the One Sith and the Fel Empire decimated half of the Jedi Order.
When Cade Skywalker arrived at the Hidden Temple, Jedi Master Tili Qua was present. He requested the Jedi High Council's assistance in assassinating Darth Krayt. Qua was also there when Roan Fel's message was delivered by his Imperial Knights, including his daughter, Princess Marasiah Fel. Fel's Knights revealed that the Emperor desired an alliance between the New Jedi Order and the Empire-in-exile to overthrow Darth Krayt's Galactic Empire. Master Qua had concerns about the Jedi allying with the Imperial Knights, given Roan Fel's previous war against the Jedi and his alliance with the Sith, which led to the Order's destruction.
When the Jedi Council agreed to allow Darth Krayt's reborn forces to attack the Hidden Temple, Master Qua was present with the rest of the council. This was a strategic move to allow Admiral Gar Stazi's fleet and Fel's fleet to ambush the Sith-Imperial fleet and inflict a significant blow to the Sith Empire. As Darth Krayt's Dragon ships began to devastate the allied fleets, Master Qua evacuated the Hidden Temple on a vessel carrying the Jedi younglings, urging them to use the Force to overcome their fear.
After the surviving ships of the allied fleet reached Bastion, Master Qua traveled to the planet's surface and examined the autopsy of one of Darth Krayt's new Sith troopers, who had been captured by Cade Skywalker. The trooper claimed to be just one of millions serving Krayt before he died, leading Masters Qua and K'Kruhk to agree to an attack on Coruscant in an attempt to defeat Krayt before he could gain control of the entire galaxy.
During the battle, Cade Skywalker killed Darth Krayt, but Roan Fel also died when he tried to purge all life on the planet in an attempt to win it, and his Imperial Knights were forced to stop him. Tili Qua, among other Jedi, attended the late Emperor's funeral, while K'Kruhk was chosen to represent the Jedi as a Triumvir in the newly established Galactic Federation Triumvirate.