Publicise in an exaggerated way (4)

I believe the answer is:

hype

(Other definitions for hype that I've seen before include "Slang for extravagant promotion of a product" , "Ballyhoo" , "Overblown publicity" , "Salesman's exaggeration" , "Extravagant publicity or promotion" .)

I've seen this clue in The Guardian.

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