The Quorum of Ships' Captains is the legislative body that replaces the Quorum of Twelve after the events of Gaeta's Mutiny.
Instead of reforming the colony-based Quorum with new representatives, Lee Adama proposes that the Colonials not be represented according to their extinct home colonies, but rather according to the ships they live on. President Roslin supports the idea and tasks Lee with restructuring the civilian government accordingly (TRS: "No Exit").
A new Quorum is formed, this time made up of ship's captains. It is unknown how many captains are on this new Quorum, but it is known that a Cylon representative, a Six named Sonja, has been elected to this Quorum to represent the Rebel Basestar (TRS: "Someone to Watch Over Me"). Doyle Franks, Xeno Fenner, and Greene are also members (TRS: "Islanded in a Stream of Stars").
It is presumed to be dissolved after the Colonials reached the new Earth (TRS: "Daybreak, Part II").