Primarch (偉大法王, Idai Hōō?, lit. "Great Pope") is the head of the government, the Sanctum, in Final Fantasy XIII. Galenth Dysley is the current Primarch at the game's start, though he later resigns. The Primarch is the head and representative of the Sanctum, and is said to be the one to communicate with the fal'Cie Eden who gives advice and guidance, but restrains from direct influence.
At the game's start the current Primarch is Galenth Dysley, an elderly man who appears deeply concerned over Cocoon's citizens. His voice can be heard broadcast over the loudspeakers during the Purge explaining its necessity, and he is later shown appearing on TV saying basically the same thing.
It is later revealed that Dysley is nothing but an avatar for the fal'Cie Barthandelus, proving the position of Primarch nothing but a puppet position. Dysley later resigns and places Cid Raines as the new Primarch in line, however, Raines, having been made Barthandelus's l'Cie, is only playing a role in Barthandelus's plan to lure the fugitive Pulse l'Cie back into Cocoon. Raines is eventually killed by the Cavalry.