Composer exaggerated when naked (5)
I believe the answer is:
verdi
'composer' is the definition.
(Italian composer Giuseppe Verdi)
'exaggerated when naked' is the wordplay.
'exaggerated' becomes 'overdid' ('overdo' can be a synonym of 'exaggerate').
'when naked' says to take the centre.
The middle letters of 'overdid' are 'VERDI'.
(Other definitions for verdi that I've seen before include "Drive around with great opera composer" , "Composer of opera ''Rigoletto''" , "Drive around to locate opera composer" , "Giuseppe -----, 1813-1901, prolific opera composer" , "Italian composer (Aida)" .)