Sector 004 was a region of space. A section of the Romulan Neutral Zone was located in Sector 004/11.

In 2364, the Federation starships USS Tranquillity Base, USS Max Plank, and USS Non Sequitur and the starbase Starbase Trailer Twenty-Nine were ordered by Starfleet Command to decrease sensor drone surveillance of this sector. This sector was mentioned in mission orders. (TNG: "Conspiracy", okudagrams)

This sector was only mentioned in writing.
According to Star Trek: Star Charts (pp. 18 & 19), the Sigma Draconis system was located in this sector, which was also known as the Sigma Draconis sector.
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