The Klystron are a species native to either the Alpha or Beta Quadrant. The Klystron ambassador was present at the trade conference at Deep Space 9 in 2370. Gul Marak came aboard the space station and tried to convince the Klystron ambassador that they would prosper more if the Cardassians were in control of the region again. (DS9 novel: Betrayal)

Given that there were many species present for the trade conference, it's possible that the Klystron were from the Gamma Quadrant. However, it's also possible that the author simply misspelled Klaestron.