Celestial Intervention Agency

The Celestial Intervention Agency or CIA was a secretive Time Lord organisation with whom the Doctor and Lord President Romana occasionally had dealings. Its motto — "the story changes, the ending stays the same" —  was also a modus operandi. According to the Fifth Doctor, CIA operatives protected the web of time by ensuring, by whatever means, that the net result of history remained constant, even though details might change. (AUDIO: The Kingmaker) Because they often violated the Time Lords' non-interference policy, they had to operate in secret so as to give plausible deniability to the High Council. (PROSE: World Game)

Origins and nature
The CIA were a group created as a covert arm of the High Council to safeguard the Time Lords' interests. (HOMEVID: Shada) They evolved from a core group of Rassilon's guards. (PROSE: Lungbarrow) They functioned as spies. It was said that they "don't even know which side they're on." (AUDIO: Mindbomb)

CIA's involvement with the Doctor
The CIA first employed the Second Doctor to work for them following his trial for breaking the non-interference policy. The Doctor reluctantly agreed to go on a mission with the Time Lady Serena against the Players. After they completed that mission, he was assigned to go with Jamie McCrimmon at his side to Space Station Camera to persuade Dastari to discontinue Kartz and Reimer's time travel experiments. (PROSE: World Game, TV: The Two Doctors)

The Third Doctor, made to regenerate against his will, was exiled to Earth. (TV: Spearhead from Space onward) Though this remains speculative, it seems very possible that the CIA sent the Third Doctor to Uxarieus to prevent from obtaining the Doomsday Weapon. (TV: Colony in Space), to Peladon to assist in its joining the Galactic Federation (TV: The Curse of Peladon) and to Solos in the 30th century to deliver a package from the Time Lords. (TV: The Mutants)

The Third Doctor was reprieved following his defeat of Omega. (TV: The Three Doctors) The Time Lords would continue to use him as an agent.

It was a Time Lord by the name of Lord Ferain who appeared to the Fourth Doctor to send him on a mission to Skaro to avert the creation of the Daleks. (PROSE: Lungbarrow, TV: Genesis of the Daleks)

The Doctor suspected that the Time Lords (probably the CIA) sent him to Karn to prevent ex-Gallifreyan president Morbius being resurrected by Dr. Mehendri Solon (TV: The Brain of Morbius).

The Sixth Doctor also suspected the Time Lords of using him to try to stop the Cybermen from altering history by destroying Earth in 1985. (TV: Attack of the Cybermen)

Co-ordinator Vansell of the CIA, saw that the Doctor's actions had allowed the Nestene Consciousness to escape destruction and saw to it that a trial for him would take place on Space Station Zenobia. (PROSE: Synthespians™) After the transportation of the Doctor's TARDIS to the space station (TV: The Mysterious Planet) and the presentation of evidence (TV: The Mysterious Planet, Mindwarp, Terror of the Vervoids), the trial concluded with the Doctor's prosecutor, the Valeyard, exposed as the Doctor's own corrupt future self, the Doctor exonerated and political unrest on Gallifrey. (TV: The Ultimate Foe)

During the final times of the Last Great Time War, Rassilon sent a group of agents of the CIA along with Karlax, who had the mission to kill the War Doctor because of his opposition to the plans of the High Council. Before they could accomplish it, the agents died when their Battle TARDISes were all destroyed by the sudden attack of Dalek stealth ships. (PROSE: Engines of War)

Other projects and missions
The CIA sent a Time Lord as their agent to Apertsu to serve as a security consultant; however, he was captured by Aubertides who wanted the secret of regeneration. (PROSE: Human Nature)

The CIA began to fear the number of temporally active races, so they began experimenting with various temporal technologies, including the TARDISes, in an attempt to move the minds of (newly created) TARDISes within the minds of aliens taken from over 50 planets. Time Lady Professor Klyst oversaw this experiment. (AUDIO: Unregenerate!)

The CIA sent a Time Lord to Jamie McCrimmon in order to correct a fluctuation in the time line caused when Jamie tried to help King James II of England. (AUDIO: The Glorious Revolution)

The CIA and the war
President Romana sent the CIA agents Gandarotethetledrax and Cavisadoratrelundar to observe/create the first Type 102 TARDIS (knowing that it would be a vital piece of technology in the upcoming war), and witnessed the former Remote agent Compassion complete a transition to a sentient TARDIS. They were halted by the people of the Catuvalani. The Eighth Doctor escaped with the Type 102 TARDIS. (PROSE: The Shadows of Avalon)

At some point in the lead-up to the War, the CIA became worried that they might be erased from history (or caught in the crossfire) between the Time Lords and the Enemy, and therefore created Mictlan, a world outside of time and the universe for themselves to hide within. However, they also needed to remove themselves from the universe of physicality, and therefore turned themselves into The Celestis. (PROSE: Alien Bodies, The Taking of Planet 5, Interference)

Leadership
Sentris was head of the CIA for a time before discovering how many people she had sent to the Oubliette of Eternity. Upon discovering the number, she threw herself into it. (AUDIO: Neverland)

Coordinator Harom was head of the CIA for an unknown period of time. (AUDIO: Urban Myths)

Coordinator Rigan was head of the CIA whilst the experimentation on species for TARDIS pilots using Block Transfer Computation. (AUDIO: Unregenerate!)

Coordinator Vansell was head of the CIA during Romana's presidency until he encountered the Neverpeople. (AUDIO: Neverland)

Coordinator Narvin took over as head of the CIA following Vansell's death aboard the time station. (AUDIO: Neverland)

Bulek was head of the CIA during the resurrection of Morbius. (AUDIO: Sisters of the Flame,The Vengeance of Morbius)

Higher-ups

 * Coordinator Sentris
 * Coordinator Vansell
 * Coordinator Narvin
 * Coordinator Rigan
 * Coordinator Straxus
 * Director of Allegiance Ferain
 * The Voice of the Agency
 * President Niroc
 * Councillor Sardon
 * Councillor Ortan
 * Councillor Ratisbon
 * Almoner Crest Yeux
 * Bulek

Agents

 * Commander Torvald
 * Gandar
 * Cavis
 * Glospin
 * Mortimus
 * Serena
 * Kurst
 * Levith
 * The Doctor (Reluctant agent from second through sixth incarnations)

CIA assets
The CIA developed psychic paper technology. (PROSE: World Game)

Space Station Zenobia (the location of the the Sixth Doctor's trial) was the property of the CIA. (PROSE: The Eight Doctors)

The Oubliette of Eternity a device which was supposed to remove people from history, but instead made them Neverpeople. (AUDIO: Neverland)

They possessed a Vortex Ops unit which scanned the Time Vortex for any anomalies. (AUDIO: Weapon of Choice)

Behind the scenes

 * Doctor Who writer and Script Editor Robert Holmes introduced the CIA in the "revisionist" story The Deadly Assassin, in order to address the contradiction between the Time Lord's non-interference policy and the Doctor having gone on missions for them. According to Holmes, then, all of the Doctor's previous missions took place on behalf of the CIA.
 * He used the acronym CIA as a reference to the Central Intelligence Agency, which in the real world would engage in covert activities outside of US soil while also maintaining "plausible deniability". He conceived of the Time Lords as corrupt and maintained that they worked in the same way.