Originally thought of in the Oriental sense Monk’s have long since become mainline character classes in D&D, indeed the european monk (or friar if you will) is more suited to the abilities of the cleric.
Unearthed Arcana present two more monastic traditions whose path your monk may tread:
Way of the Kensei
These warrior monks train ceaselessly with their weapon, making it an extension on themselves. Back in 1st Edition Oriental Adventures, the Kensei was a separate class of its own, but here its presented as a more martial approach to the monastic lifestyle.
Way of Tranquility
In almost total opposition to the Kensei, the way of tranquility presents a tradition that views violence as a last resort. Diplomacy and healing being just two of its aspects, but don’t be fooled, while they prefer a peaceful solution sometimes the only answer is a violent one and these monks are nobodys fool.
As always these aren’t legal for use in your Adventurer’s League games but I heartily encourage you to try them out in your home games and when the survey for them is posted (usually Monday or Tuesday over on the Wizards website) leave your feedback and maybe we’ll see your suggestions put into play in a future supplement.