Theatrical and exaggerated Frenchman in beret (4)
I believe the answer is:
camp
'theatrical and exaggerated' is the definition.
(camp can mean affected or theatrical)
'frenchman in beret' is the wordplay.
'frenchman' becomes 'm' (abbreviation for Monsieur - like 'Mr').
'in' is an insertion indicator.
'beret' becomes 'cap' (beret is a type of cap).
'm' inserted within 'cap' is 'CAMP'.
(Other definitions for camp that I've seen before include "Place where people live in tents" , "somewhat affected" , "Live in a tent" , "Wildly theatrical" , "Foppish" .)