Apple-polish is an idiom and a compound word.
To apple-polish means to present a small token in order to ingratiate oneself, to flatter a superior in order to obtain a favor or an advantage in a situation. Synonyms of apple-polish that may be found in a thesaurus are fawn, kowtow, brown-nose. The word apple-polish first appears in print in the United States in the 1920s, but most probably existed for a period of time before that date. Apple-polish is the verb form, related words are apple-polishes, apple-polished, apple-polishing. The nouns apple-polishing and apple-polisher are probably the more commonly used forms of the idiom. Apple-polisher seems to have started in the schoolyard as an epithet for a child who was attempting to curry favor with the teacher, based on the practice of bringing an apple to a teacher as a gift. If a child were trying to elicit good feelings in his teacher, he would surely polish the apple to a high sheen and present it to her as a treasure. Note that according to the Oxford English Dictionary, apple-polish and related words should be spelled with a hyphen.
There are countless words in English for a person who is given to fawning, self-serving flattery of others, and they are all vivid: “brownnoser,” “bootlicker,” “apple-polisher.” (Publishers Weekly)
By the time American scholar Jan Harold Brunvand published his book, The Study of American Folklore, in 1968, the phrase “apple-polisher” was more or less shorthand for brown-nosing suck-up. (The Smithsonian)
“Boy, he sure did a lot of apple polishing early on and with all those guest he had to chat about and have stand up, I thought his speech would never end,” Garvin said. (The Cleburne Times Review)