In the Star Trek universe, the Gamma Quadrant is 1/4 of the Milky Way, usually oriented in the upper-right on maps of the galaxy.
Exploration of the Gamma Quadrant opened up to the Federation upon the discovery of the Bajoran wormhole providing a stable route 70 000 light-years from near Bajor in the Alpha Quadrant to the Idran system.
The dominant power (known to us) there is the Dominion, though following their defeat in 2375, the political climate may change.
Notable species from the Gamma Quadrant include the Founders, the Jem'Hadar, and the Vorta.