After Section 31 caused the Lantru disaster while trying to stabilize the Omega Molecule, Captain James T. Kirk called several trusted officers to a meeting on an uninhabited planet. With Kirk, these officers - including Phil Waterson, Nick Silver, Aaron Stone, and José I. Mendez - formed a cabal to monitor and oppose Section 31.
Like Section 31, this cabal operated in secret, hidden from the United Federation of Planets at large and most of Starfleet. Membership in the cabal was by invitation only.
The Kirk Cabal still existed in the late 24th century. By then Starfleet Intelligence operative Elias Vaughn was a member of the cabal, and due to his efforts to oppose 31 Dr. Julian Bashir was invited by Vaughn to also join the cabal.
By the early 25th century much of Section 31 was exposed to the public, and 31 was finally brought down. With their goal successful, the Kirk Cabal disbanded at this time.