Q in a Franciscan monk's garb, wielding a rosary
A monk was a member of a religious order. Traditionally, this term was applied to a person who lived in a monastery.
Monks were known in such races as Vulcans, Bajorans, Humans, and Kadi and imitated by Q during an appearance to the crew of the USS Enterprise-D in 2364. (ENT: "The Andorian Incident"; TNG: "Hide And Q"; DS9: "In the Hands of the Prophets"; VOY: "Someone to Watch Over Me")
In the Bajoran religion, vedeks, prylars, and ranjens were also called monks. (DS9: "Emissary", "In the Hands of the Prophets", "The Collaborator", "The Darkness and the Light", "The Reckoning")
In 2365, Lieutenant Commander Data told a joke to Guinan which began as "a monk, a clone, and a Ferengi decide to go bowling together". (TNG: "The Outrageous Okona")
In late 2369, Vedek Bareil Antos told Commander Benjamin Sisko that he knew a monk, when he was five years old, who could "squeeze the pagh right out of your ear with his thumb and forefinger". (DS9: "In the Hands of the Prophets")
Silent monks were mentioned in the Vulcan tale of enlightenment "Falor's Journey". (VOY: "Innocence")
In a holoprogram set in 16th century Florence, Leonardo da Vinci had to deliver a bronzetto to the monks at Santa Croce and asked Catarina to accompany him and pray there. (VOY: "Scorpion")
The cover for the DVD for TNG: "The Ensigns of Command" shows Data with the 14th Dalai Lama and his entourage, who visited the set during the filming of the episode and had pictures taken with Brent Spiner.