(covers information from several alternate timelines)
Sector 45 was a region of space in the Beta Quadrant. A section of the Romulan Neutral Zone was located in Sector 045/34. The Federation was monitoring Romulan operations in 045/3195.
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 increase sensor drone surveillance of this sector. Starbase 245 was ordered to cease monitoring a section of this sector, and turned this task over to the sensor drones. This sector was mentioned in mission orders. (TNG: "Conspiracy", okudagrams)
In the alternate 2259, the Neutral Zone, located in this sector, was being monitored for activity by Starfleet. Results from this intelligence gathering were displayed on a galactic map, with its focus primarily on the Alpha Quadrant, which was in a collection of graphics and video media that were seen on a powerwall in the offices of Admirals Christopher Pike and Alexander Marcus at Starfleet Headquarters. (Star Trek Into Darkness)