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Depnding on what you mean by "Someone" but assuming you mean any sentient lifeform:

The Doctor has stated on a number of occasions that he has killed when necessary, and there have been a few on-screen examples.

For example, although "The Day of the Doctor" now confirms that he did not kill the Timelords to resolve the Time War, he did orchestrate the circumstance in such a way that billions of Daleks killed each other. We also see the Doctor directly kill Daleks in a number of storylines, such as "Remembrance of the Daleks", during which he also arranges for the planet Skaro to be destroyed at some point in its history.

In "The Brain of Morbius", we actually see the Doctor kill in cold blood as he assassinates Solon using poison gas. A similarly controversial killing occurs when the Sixth Doctor smothers the Androgum in "The Two Doctors". He also shoots a number of Sontarans in "The Invasion of Time" and a Cyberman in "Attack of the Cybermen". More recently, in "Dinosaurs on a Spaceship", the Doctor deliberately left the marauder Solomon on his small space craft to be shot down by rockets rather than rescue him. However, The Doctor had given Solomon the chance to leave the spacecraft and Solomon refused.