In 2256, the system's location was labeled on the star chart "Alpha/Beta Quadrant Overview" in the ready room aboard the USS Discovery. It was located in territory claimed by the Klingon Empire. (DIS: "Magic to Make the Sanest Man Go Mad", "The War Without, The War Within")
In 2368, Jean-Luc Picard's blockade fleet retreated to this system to regroup, following the disabling of their tachyon detection grid, seeking to establish a new grid. However, this proved unnecessary as the USS Sutherland detected the Romulan forces by another method. (TNG: "Redemption II")
In 2399, the system's location was labeled on a Federation star chart that was in Fleet Admiral Kirsten Clancy's office at Starfleet Headquarters. It was located in neutral space. (PIC: "Maps and Legends")
According to Star Trek: Star Charts (p. 62) and Stellar Cartography: The Starfleet Reference Library ("Stellar Cartography", pp. 27, 30; "Federation Historical Highlights, 2161-2385"), Gamma Eridon was a binary star system with a pair of M-class stars. According to a map of the Klingon Empire – prepared by the Scribe K'Tark for the Klingon High Council in the Year of Kahless 893 (2266) – Gamma Eridon was identified as a Klingon system.