Within Starfleet, the Fleet chief engineer is a title given to an Engineering officer responsible for the engine rooms of a fleet of ships. Unlike the Chief engineer, the Fleet chief reports directly to the Fleet Commander and is not solely responsible for Engineering on one vessel. Quite often they will operate out of one engine room and communicate with the Chief Engineer of the other ships, who in some cases report directly to the Fleet chief engineer.
In Project Full Circle, Lieutenant commander B'Elanna Torres became the Fleet chief of the USS Voyager, USS Esquiline, USS Quirinal, USS Hawking, USS Curie, USS Planck, USS Galen, USS Achilles, and the USS Demeter. (VOY novel: Full Circle)
Later, the USS Vesta joined the fleet after the destruction of the Esquiline, Quirinal, Hawking, Curie and the Planck. Thus, Vesta's engine room became Torres's responsibility. (VOY novel: Protectors)