tricky wrestler; shrewd fellow
Originally a sumo term for a wrestler who wins with clever techniques rather than brute strength. By extension, a person who is cunning, resourceful, or skilled at outmaneuvering others.
He is a famous tricky wrestler in the sumo world.
あの政治家はなかなかの業師で、いつも巧みに議論をかわす。
That politician is quite a shrewd fellow, always skillfully dodging arguments.
underhanded person; Machiavellian schemer
Compound of 業 (わざ, 'technique, trick') and 師 (し, 'master, specialist'). The exact historical derivation is uncertain, but the term is strongly associated with sumo.