Green’s Dictionary of Slang

(orig. US) to curry favour, to toady.

1931		L.A. Times 13 Dec. III 1/5: Miss Price, that’s our instructor, you know, the one that is simply adorable, well anyway, all the boys try to apple-polish her into giving them a good grade.
1939		R. Chandler ‘Trouble Is My Business’ in Spanish Blood (1946) 183: Why try to apple-polish the dinge downstairs?
1943		F.E. Long Clearing House 76: How can I apple-polish the boss (or college professor)? [...] How much lipstick should I wear to have people like me?
1944		Slanguage Dict. Mod. Amer. Sl.
1953		T. Runyon In For Life 282: I refused to have anything in the Presidio that might sound like apple-polishing.
1963		Dundes & Schonhorn ‘Kansas University Sl.: A New Generation’ in AS XXXVIII:3 169: To curry favor with a professor: apple polish.
1967–8		Baker et al. CUSS 71: Apple polish Curry favor with a professor.