Cor — heartless newspaper boss — you must give that person their due! (8)
I believe the answer is:
creditor
'you must give that person their due' is the definition.
(someone due a payment from you)
'cor heartless newspaper boss' is the wordplay.
'heartless' suggests removing the centre.
'newspaper boss' becomes 'editor' (newspaper editor).
'cor' with its centre taken out is 'cr'.
'cr'+'editor'='CREDITOR'
(Other definitions for creditor that I've seen before include "Person to whom debt is owed" , "One who's owed money" , "Person owed money by director" , "Director (anag)" , "He's the one owed the money" .)