Zibal, also known as Zeta Eridani, was a star system in the Alpha Quadrant.
Alpha/Beta Quadrant Overview
In 2256, the location of Zibal was labeled on the star chart "Alpha/Beta Quadrant Overview" in the ready room aboard the USS Discovery. (DIS: "Magic to Make the Sanest Man Go Mad") During the Klingon War, Zibal was included on force movement star charts during the Battle of J'Gal. (SNW: "Under the Cloak of War")
In 2259, the location of this system was labeled on a stellar cartography chart that was seen on the USS Enterprise's ready room viewscreen. This system's symbol had a blue color, indicating that it was affiliated with the United Federation of Planets. (SNW: "Strange New Worlds", "Children of the Comet", "Spock Amok")
The system's location was labeled in a Federation star chart that was in Fleet Admiral Kirsten Clancy's office at Starfleet Headquarters in 2399 and on the bridge of the USS Titan in 2401. The Zibal system was in or near to neutral space. (PIC: "Maps and Legends", "The Next Generation", "Disengage")
This star system was only mentioned in writing.
According to Star Trek: Star Charts (p. 62) and Stellar Cartography: The Starfleet Reference Library ("Federation Historical Highlights, 2161-2385"), Zibal (Zeta Eridani) consisted of a pair of A-class stars.