Old age was the latter stage of a lifespan prior to death, and could be referred to as the natural cause of it.
In New York, Rory Williams witnessed a version of himself from an alternate future die of old age, having been sent back in time by a Weeping Angel. (TV: The Angels Take Manhattan)
The Eleventh Doctor, having expended all twelve of his regenerations, was left at the brink of "dying of old age" as the Siege of Trenzalore reached its conclusion. He was, however, enabled to regenerate once more after being provided with additional regeneration energy "love from Gallifrey". (TV: The Time of the Doctor)