Quadrant 9 was a region of space in the Alpha Quadrant. It included a portion of the Romulan Neutral Zone. This quadrant was distant from Ferengi territory, and the Romulans had left this quadrant and hadn't returned by 2364. In that year, Starfleet reported a disturbance in the quadrant and had requested the USS Enterprise to investigate. During its investigation, the Federation starship came upon the freighter Batris in section 7 of the quadrant. In its questioning of the survivors from the freighter, the Enterprise determined that the disturbance was a battle between the freighter Batris and the cruiser IKS T'Acog. (TNG: "Heart of Glory")
This use of the term quadrant occurred before the current standardization of the quadrant/sector model of stellar cartography.