Right winger the heart of Athletic (5)
I believe the answer is:
title
'right' is the definition.
(title is a kind of right)
'winger the heart of athletic' is the wordplay.
'winger' becomes 'tit' (tit is a kind of bird).
'the heart of' means to look at the middle letters.
The middle of 'athletic' is 'le'.
'tit'+'le'='TITLE'
(Other definitions for title that I've seen before include "Book's name" , "big role" , "Lord, sir or doctor, say" , "Appellation signifying status or function" , "Distinctive name" .)