As a detective solving the mystery of the crossword clue ‘Insulating sleeve for a beverage‘, the key insight was to think about what kind of item would fit that description. Firstly, the word ‘insulating‘ suggests it’s something that keeps a beverage cold or hot. Then, the clue says ‘sleeve‘, which implies it’s a kind of cover that slides over an item. Finally, thinking about the common slang term for a beer or soda can, which is ‘brewski‘, I realized that a KOOZIE would fit the description perfectly. A KOOZIE is a cylinder-shaped insulating sleeve made from foam, neoprene or other materials that can keep cans or bottles cold for longer periods. It was a light bulb moment, and the answer to the crossword puzzle was solved!