Sector 007 was a region of space. A portion of the Romulan Neutral Zone was located in this sector. In 2365, the Federation starship USS Endeavour was assigned a deep space exploration mission in this sector. (TNG: "Conspiracy", "The Measure Of A Man"}
The sector was never mentioned in dialog; it was mentioned on a Starship Deploy Status seen in Starbase 173.
", Sector 007 was implied to be in a range of sectors (004 to 010) in which segments of the Neutral Zone were located.