- You may be looking for the Time Lord known as the Monk.
A monk was a male member of a religious order. Many different religions had monks as a part of their ecclesiastical structure. Monks of whatever religion typically resided at a monastery. The Doctor had many encounters with monks over the course of his lifetime. (TV: The Abominable Snowmen, Tooth and Claw, A Good Man Goes to War, The Bells of Saint John, The Rings of Akhaten, AUDIO: The Book of Kells, COMIC: Dragon's Claw)
One Time Lord was so enamoured of monks that he adopted their title as his name to become "the Monk". He followed the examples of the Doctor and the Master in taking his name from a generic title. (TV: The Time Meddler, AUDIO: The Book of Kells)
The adherents of the Order of the Headless were known as the "headless monks" due to their appearance. They believed that the domain of faith was the heart and the domain of doubt was the head, so they chose to have themselves beheaded. (TV: A Good Man Goes to War) Some soldiers were also volunteered at Demons Run to join the Order of the Headless.