Old English clingan "hold fast, adhere closely; congeal, shrivel" (strong verb, past tense clang, past participle clungen), from Proto-Germanic *klingg- (cf. Danish klynge "to cluster;" Old High German klinga "narrow gorge;" Old Norse klengjask "press onward;" Danish klinke, Dutch klinken "to clench;" German Klinke "latch").
The main sense shifted in Middle English to "adhere to" (something else), "stick together." Of persons in embrace, c.1600. Figuratively (to hopes, outmoded ideas, etc.), from 1580s. Of clothes from 1792. Related: Clung; clinging.