Cowardly chap is after elegance and style (7)
I believe the answer is:
chicken
'cowardly' is the definition.
(chicken can informally mean cowardly)
'chap is after elegance and style' is the wordplay.
'chap' becomes 'ken' (man's name).
'is after' says to put letters next to each other.
'elegance and style' becomes 'chic' (chic can mean style or fashion).
'ken' after 'chic' is 'CHICKEN'.
(Other definitions for chicken that I've seen before include "Keep the creature in check" , "Domestic bird - frightened" , "Reckless game" , "Prov. cowardly bird" , "Informally cowardly like domestic fowl" .)