The Athlete
by Marc SaindonMonk Monastic tradition suggestion for the Milenian Empire: the Athlete
I've checked a few peplum D&D rpg (notably Arkadia) and a common monk adaptation seems to be Monk = Gladiator, which seems to me like Ancient Grome (not a problem in itself) more than Ancient Greece.
An alternative would be that the Milenian Empire produces a few dedicated Olympic Athletes. They have a harsh code of sportsmanship, rigorous training, training facilities (gymnasiums), trainers for sensei/student rapport, competitions, and a wide variety of disciplines (disk throwing, sprint, javeline, wrestling) that require specialized techniques. Most athletes will probably be just from the Fighter class, but the really dedicated ones could emulate Monks.
Ki becomes Pneuma ('breath'). Martial Arts becomes Pankration (the ancestor of MMA). Unarmored Movement is the result of years of training as a sprinter.