(covers information from several alternate timelines)
Sector 034 was a region of space.
In 2365, the Federation starship USS Excelsior was assigned a deep space exploration mission of this sector. The sector was listed on the Starship Deploy Status chart that was on display in the courtroom of Starbase 173. (TNG: "The Measure Of A Man", okudagram)
In the alternate 2259, this sector was labeled on a map of the Alpha Quadrant. This map 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)