Gamma Hydra II was the second planet orbiting Gamma Hydra. This planet was located in both the administrative area of Starbase 10 and the Gamma Hydra sector.

When crewmembers of the USS Enterprise, including Captain Kirk were afflicted by radiation on Gamma Hydra IV, causing them to age rapidly, Kirk several times mistakenly stated that the Enterprise orbited Gamma Hydra II because of the decreased mental capabilities due to his "old age". (TOS: "The Deadly Years")

This planet was only mentioned in dialogue.
According to Star Trek: Star Charts (p. 56, "United Federation of Planets II") and Stellar Cartography: The Starfleet Reference Library ("Federation Historical Highlights, 2161-2385"), the Gamma Hydra system was located in the Beta Quadrant.
The Star Trek Encyclopedia (4th ed., vol. 1, p. 296) located Gamma Hydra IV, a sister planet to Gamma Hydra II, in the Gamma Hydra system.