Green’s Dictionary of Slang

(orig. US) influential, important; ‘classy’.

1882		Nat. Police Gaz. (NY) 11 Nov. 3/2: They did the high-up style of airs to the queen’s taste and looked down on the American fakes [...] in a supercilious way that was most expressive of exalted manner and position.
1917		Van Loan ‘Eliphaz, Late Fairfax’ in Old Man Curry 154: He’s a crook [p...] but he’s got high-up friends.
1918		K.F. Purdon Dinny on the Doorstep 92: A train was coming along with some high-up Quality, directors or the like of that.
1959		G. Sparrow Great Swindlers 123: [A] high-up army officer, or a high-up police official .
1969		B. Mason Awatea (1978) 29: You may be a high-up police feller, but you don’t know the rules!
1973		H. Leonard Da (1981) Act I: Sure you couldn’t let him mix with high-up people and the arse out of his trousers.
1989		H. Leonard Out After Dark 63: She said [...] she would treat us to the kind of ice-cream high-up people ate out of tubs with wooden spoons.