Hamlet perhaps right -- terrible loser with no heart (5,4)
I believe the answer is:
title role
'hamlet perhaps' is the definition.
(Hamlet is the title role in Shakespeare's play)
'right terrible loser with no heart' is the wordplay.
'right' becomes 'title' (title is a kind of right).
'terrible' is an anagram indicator.
'with no heart' suggests removing the centre.
'loser' with its centre taken out is 'loer'.
'loer' anagrammed gives 'role'.
'title'+'role'='TITLE-ROLE'
(Other definitions for title role that I've seen before include "Eponymous part in play" , "Hamlet in Hamlet, say" , "Main part of a story" , "taken by Lear amongst others" , "Main part in play" .)