Quadrant 9 was a region of space. A segment of the Neutral Zone was located in this quadrant, which was far away from Ferengi Alliance territory. As of 2364, there hadn't been any recent Romulan presence in the sector.
During that year, Starfleet detected a disturbance in the quadrant at coordinates 070-mark-3 and requested the USS Enterprise to investigate. At the conclusion of its investigation, the crew of the Enterprise-D determined that the disturbance was a battle between the commandeered freighter Batris and the cruiser IKS T'Acog. (TNG: "Heart of Glory")
In the dialogue, the terms "Quadrant 907-mark-3" and "Quadrant 9, coordinates 070-mark-3" were used interchangeably.