The Time Agency was an organisation founded to fill the vacuum of power left by the Time Lords after the Last Great Time War. (COMIC: Weapons of Past Destruction) It originated around the 49th century and was shut down some time after the 52nd century. (TV: Kiss Kiss, Bang Bang) The Agency employed humans called Time Agents. The Agents used vortex manipulators which enabled them to travel through time for missions of an unspecified nature.
One account stated that, "The Agents' purpose is to change without interfering, to leave an effect with no evidence of cause. To be untraceable, undetectable, invisible. To all intents and purposes, the Agents do not exist." (PROSE: Sometime Never...)
By the Thirteenth Doctor's time of life, the Doctor was well acquainted with the Time Agency. She had enough influence to convince them to hire Dr Irene Schulz and Dr Leon Perkins after the pair displayed initiative and aptitude in the course of a shared adventure. (COMIC: A New Beginning)
To fill the power vacuum left by the Time Lords' disappearance after the Last Great Time War, (COMIC: Weapons of Past Destruction) the Time Agency was set up at some point after the 42nd century, as the Agency set up time treaties back in time up to the 42nd century. [statement unclear] (AUDIO: The Time Machine)
Magnus Greel, a war criminal from the 51st century, lived in fear of Time Agents, initially suspecting the Fourth Doctor of being one until Li H'sen Chang mentioned the Doctor had asked questions. "A Time Agent wouldn't have asked questions!" exclaimed Greel. "A Time Agent would know." (TV: The Talons of Weng-Chiang) Greel had only heard about the Time Agents from the Fifth Doctor. To avoid revealing his identity before Greel encountered him in the late 19th century, the Doctor claimed he was a Time Agent. (AUDIO: The Butcher of Brisbane)
Adam Mitchell sent a distress signal through time using Cyberman technology. Neal Shaw was sent to investigate the signal, but was frozen in time by Mitchell. The Eleventh Doctor freed Shaw, and Shaw returned to duty after giving the Doctor a way to track his vortex manipulator through time. (COMIC: Mystery Date, The Choice)
Jack Harkness, a member of the Time Agency, was from the Boeshane Peninsula. This was a matter of great pride to the other citizens of the Peninsula, as he was the first of them to join the agency. They began calling him the "Face of Boe". (TV: Last of the Time Lords) As an Agent, he worked with John Hart, also known as "Captain John". (TV: Kiss Kiss, Bang Bang) After the Agency wiped two years of his memory for unknown reasons, he left the Agency and struck out on his own as a con man and freebooter. (TV: The Doctor Dances) He later became a companion of the Ninth and Tenth Doctor and leader of Torchwood Three. His vortex manipulator proved instrumental in his adventures. (TV: The Doctor Dances, Everything Changes, Utopia et al.)
In 5145, River Song acquired a vortex manipulator from the black market that was "fresh off the wrist of a handsome Time Agent". The wrist-strap was presented still on the wrist, until Dorium Maldovar had it removed. The vortex manipulator ended up proving vital to saving the universe, and was used by both River and the Eleventh Doctor. (TV: The Pandorica Opens, The Big Bang) Despite being imprisoned in Stormcage Containment Facility, River somehow hung onto the manipulator and used it during her further travels. (TV: A Good Man Goes to War, The Angels Take Manhattan)