Green’s Dictionary of Slang

(US) a superior or important person, whether in fact or through pretension.

1880		Daily Globe (St Paul, MN) 30 Jan. 1/6: The monkey monk whacks at wheat and is just perfectly terrible [...] The boss gambolier is running the deal.
1886		Dly Teleg. (Monroe, LA) 5 Mar. 2/1: Hugh J. Campbell [...] is one of the high monkey-monks, if not head Devil, himself.
1899		J. Flynt Tramping with Tramps 368: We was [...] paradin’ roun’ the hang-out as if we was the high-monkey-monks of ev’rythin’.
1904		Wash. Times (DC) 25 May 6/4: He was the King / High monkey monk among us all.
1912		Day Book (Chicago) 23 Oct. 4/1: A high monkey-monk who wants an office got next to our old friend.
1912		Day Book (Chicago) 23 Oct. 4/1: A high monkey-monk who wants an office got next to our old friend.
1916		Day Book (Chicago) 6 Apr. 8/2: Some of the school high-monkey-monks should learn and let learn.
1934		V.G. Burns Female Convict (1960) 75: All the high monkey-monks are talking about it.