The Klimae brotherhood are a group of zealot monks occupying the Kellion of the Nativity of Christ in the skete of Katounakia on Mount Athos. They are zealots of the Matthewite persuasion; more specifically the Gregorian Matthewites (followers of Metropolitan Gregory of Messina). The brotherhood is named after it's founder Elder Klemes (Clement) of Katounakia (+1997).
There is an interesting book on Amazon called Seven Years on Mount Athos: The Power of Believing, by Christos Palaskas, who spent seven years as a monk at this small hermitage: