The Time Agency was a group apparently based in the 51st century and employing Human Time Agents. It is unknown how long it existed, but it was shut down sometime in the 51st century. The Agents utilized wrist straps which enabled them to travel through time to go on missions of an unspecified nature.
Jack Harkness was a member of the Time Agency from the Boeshane Peninsula, a matter of great pride to the other citizens of the Peninsula. (DW: Last of the Time Lords). As an Agent, he worked with John Hart, also known as "Captain John". (TW: Kiss Kiss, Bang Bang) After the Agency wiped two years of his memory for unknown reasons, he decided to leave the Agency and strike out on his own as a con man and freebooter. (DW: The Doctor Dances)