Spoiler warning: Plot and/or ending details follow.
Gamma Hydra (or Gamma Hydrae) was a star in the Gamma Hydra sector of Federation space, near the Romulan Neutral Zone. The Gamma Hydra system had at least four planets. (TOS episode: "The Deadly Years") The comet Icarus IV also orbited Gamma Hydra. (ST reference: Star Charts)
The star system had an Andorian colony as of 2256. Federation Starfleet Captain Philippa Georgiou was concerned about it after the discovery of the Klingon sarcophagus ship only six light-years away. (DSC episode: "The Vulcan Hello")
In 2285, Section 14 of the Gamma Hydra system was the initial destination of the Enterprise during Saavik's Kobayashi Maru test while at Starfleet Academy. (TOS movie: Star Trek II: The Wrath of Khan) Shortly afterwards, the real Enterprise was assigned to travel to Section 14 of the Gamma Hydra system and investigate the destruction of the USS Gallant. (TOS comic: "The Wormhole Connection")
When William T. Riker attended Starfleet Academy in the 2350s, an instructor in tactics had Riker's cadet group study a six hour recording of Gamma Hydra in order to prepare them for the tedious nature of analyzing a tactical situation. (TNG comic: "Consorting With the Devil!")
Following the apparent disappearance of the USS da Vinci in 2377, Captain David Gold attempted to take the Shuttlecraft Shirley to Gamma Hydra, but after shaking a pursuer by creating a wormhole, instead ended up at Galorndon Core. (CoE eBook: The Art of the Comeback)