Old English gliu, gliw, gleow "entertainment, mirth (usually implying music); jest, play, sport," also "music" and "mockery," presumably from a Proto-Germanic *gleujam but absent in other Germanic languages except for the rare Old Norse gly "joy;" probably related to the group of Germanic words in gl- with senses of "shining; smooth; radiant; joyful" (compare glad), from PIE root *ghel- (2) "to shine." A poetry word in Old English and Middle English, obsolete c. 1500-c. 1700, it somehow found its way back to currency late 18c. In Old English, an entertainer was a gleoman (female gleo-mægden).
Glee club (1814) is from the secondary sense of "musical composition for three or more solo voices, unaccompanied, in contrasting movement" (1650s), a form of musical entertainment that flourished 1760-1830.