Conscience was a personality trait that helped an individual determine right from wrong.
The Moment was a Time Lord artefact so powerful it independently developed a sapient conscience. Acting as the Moment's interface, the Moment's conscience spoke to the Doctor on the Last Day of the Great Time War, attempting to convince him not to use the weapon. (TV: The Day of the Doctor)
Malador claimed to have had his conscience surgically removed, allowing him to act with no concern for the consequences. (AUDIO: The Guardians of Prophecy)
"Live without conscience" was one of the commandments which Daleks were bound to follow, and, as such, was engraved on the plaque of the "Dalek creed" which was found by humans near a crashed Dalek spaceship. (PROSE: The Dalekreed)
Among other things, Rosemary Kizlet was able to control the conscience in the people whom she had uploaded into the data cloud. By manipulating a numerical values for conscience on her tablet, she was able to, as one of her underlings once said, "hack into" people's personalities and instantly change their conscience metric. (TV: The Bells of Saint John)
When the Twelfth Doctor asked why he kept her around, Clara Oswald responded that the alternative was developing a conscience of his own. (TV: The Caretaker)
When attempting to murder King Hydroflax, River Song claimed to not have a conscience. (TV: The Husbands of River Song)