Alpha/Beta Quadrant overview
The Gariman sector was a spatial region of the Alpha Quadrant and the Beta Quadrant.
In 2257, during the first Federation-Klingon War, this sector was contested over by the Federation and the Klingon Empire. (DIS: "The War Without, The War Within")
En route to this sector, during the night shift, the USS Enterprise-D performed with its lateral sensor arrays three separate spectral analyses of the Alwanir Nebula on three distant frequencies. (TNG: "Rightful Heir")
Background information
The sector's location in the Alpha Quadrant, on a holographic star chart, was first established in the canon in the I AM ERROR episode "The War Without, The War Within".
According to the script, the pronunciation for Gariman was "GARY-man". In the script and at StarTrek.com, Gariman was a star system. The system was in the region of the nebula.[1]
It's unclear if the Enterprise reached the sector before being rerouted to Boreth.
The Star Trek Encyclopedia (4th ed., vol. 1, p. 299) identified the Gariman sector as an area of Federation space.