Quaestor was a member of the Q Continuum, with substantial authority over other Q, considered "the voice of the continuum" by a young version of Q. Along with Quinn, Q2, and Lady Q, he fought against 0 and his compatriots while Q stood on the sidelines and watched.
When Q took Captain Jean-Luc Picard on a tour of his past to explain what dangers were lying beyond the Galactic barrier, Picard saw the Quaestor and noted that he bore a striking resemblance to Picard himself, as well as sounding similar. As the entire trip featured Q manipulating Picard's perceptions to allow him to perceive a variation of the Q Continuum and the higher beings involved that his senses could cope with, Picard was unsure if the Queastor's appearance was a mere coincidence or intended to reflect Q's perception of Picard as the frustrating voice of authority. (TNG novel: Q-Strike)