On the periphery of Chicago staffroom, elegant insomniac applied make-up (8)

I believe the answer is:

cosmetic

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'make-up' is the definition.
(I've seen this before)

I cannot understand how the remainder of the clue works.

(Other definitions for cosmetic that I've seen before include "improving superficial appearance" , "With surface effect only" , "better looks" , "Good for appearances only" , "Beauty preparation" .)

I've seen this clue in The Irish Times.

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