A Dracon monastery was a monastic institution, at least one of which could be found on the planet Riat. The order of monks in the Dracon monastery on Riat were characterised by bright light-orange robes, tied at the center with a thick belt, and long blonde hair, at least sometimes worn in dreadlocks, some of the monks also sported beards.
In 2369 the water supply at the Dracon ministry on Riat was contaminated by an algae, which had mutated after prolonged exposure to radiation from solar flare activity on and around the planet. This contamination caused a mutation in the monks, making them violent and cannibalistic.
In that year the solar flares also caused the shuttlecraft Goddard to craft on Riat near the monastery. The crew of the shuttle sought shelter in the monastery but soon found themselves preyed upon by the monks, fighting them several times while they awaited rescue. When that rescue did come the USS Enterprise-D also brought the monks aboard to administer a cure to their mutation. (TNG comic: "Light of the Day")