Green’s Dictionary of Slang

apple-polisher n.

[the image suggests that the apple being polished is that presented to the teacher by the class goody-goody]

(orig. US) a toady, a sycophant.

[US]N.M. Butler q. in Delaware Co. Dly Times (PA) 30 Nov. 9/: A sense of humor [...] might have saved us from being obliged to [...] contemplate the ideal world as being made up of highly competent apple polishers and pencil sharpeners.
[US]Randolph & Pingry ‘Kansas University Sl.’ in AS III:3 218: Apple polisher, n. — One who hoses a prof, that is, tries to wheedle him out of a good grade.
[US]V. Carter ‘University of Missouri Sl.’ in AS VI:3 203: apple-polisher: one who is in good standing with his professors.
[US]‘F. Bonnamy’ A Rope of Sand (1947) 173: They ain’t all apple-polishers in your classes, bud?
[US]F. Elli Riot (1967) 189: The apple-polishers are startin’ to get in on the act.
[US](con. 1950s) Jacobs & Casey Grease 6: eugene: The class valedictorian [...] An apple-polisher, smug and pompous.
[US]H. Rawson Dict. of Invective (1991) 20: An apple-polisher is a flatterer [...] apparently from the custom of schoolchildren of getting in good with their teachers by presenting them with shiny apples.
posting at PHX (Phoenix, AZ) News.com 17 Apr. 🌐 Politician [...] apple polisher, back scratcher, backslapper [etc.].