Way of Oil Wrestling
Almost as long as people have been wrestling, they've been using oil to make themselves harder to catch. In cultures where oil became sacred, oil wrestling became sacred as well. Oiled wrestlers naturally means that matches tend to run long, so the tournaments became marathon-like endurance tests for all the participants. This combination of extreme athletics with spirituality give these wrestlers an unmatched zeal both on and off the wrestling pitch, including the many famous heroes who have practiced this sport.
Oil wrestling is one of the most ancient sports, boasting the world's oldest continuously running tournament. As expected, this monk tradition focuses on keeping enemies in grapples and breaking out of grapples. It allows players to enjoy the monk's mobility while remaining mobile.
3rd level
Anointed Athlete
You gain proficiency in Strength (Athletics). You may cast Grease for 2 ki, or you may cast it as a ritual for no ki. In a regulation match, the wrestlers oil each other up, a sign of their shared and solemn respect. It's such an ingrained part of the tradition that you can feel it in your aura. With enough time and concentration, you don't even need actual oil. Your ki alone is sufficient to provide the necessary ablutions.
6th level
Never Too Slippery
Magical oil applied to your body grants a modifier to all your attack and damage rolls for eight hours. The modifier is determined by rarity: 1+ for common or uncommon; +2 for rare; +3 for very rare; legendary gives +3 and lets your martial arts attacks ignore bludgeoning resistance. If multiple oils are applied to you at once, only the highest modifier applies, but if one wears off, the next highest modifier automatically takes effect. You understand wrestling, and your body understands oil. Magical oil applied to you interacts with your aura and empowers you. The stronger the magical oil, the stronger the effect will be.
Additionally, a prone enemy within your reach must succeed on a Dexterity saving throw to stand up. On a failure, they lose the movement spent and remain prone. Your enemies find everything around you inherently slippery. The oil is always with you.
11th level
Master of Oil
You may cast Freedom of Movement on yourself for 5 ki, and Grease only costs 1 ki to cast normally. Also, you ignore the effects of difficult terrain. When you don't have the strength to escape from pins or fetters, the power of your fighting spirit can break your bonds. You've become completely acclimated to oil, and its effects no longer bother you. It's only your ally now, never a foe.
17th level
48 Hour Wrestling Matches During the Holy Fast
You gain proficiency on Constitution saving throws. You can make a Constitution saving throw any time you would otherwise suffer a level of exhaustion. On a success, you do not suffer the exhaustion. If you suffer multiple levels from a single effect, the save only cancels one. You have experienced one of the most grueling sporting events known. Compared to the exertion of the oil wrestling tournaments, the adventuring life has very little to offer that can tire you.
You may cast Grease normally for no ki. You are a true oil wrestler. The sacred oil has fully become one with your aura.
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Way of the House of Strength is culturally closely related to this tradition. Way of Harmony also offers a combination of grappling and spirituality.