That chap's right-wing past (7)
I believe the answer is:
history
'past' is the definition.
(I've seen this before)
'that chap's right-wing' is the wordplay.
'that chap's' becomes 'his' (I've seen this before).
'right-wing' becomes 'tory'.
'his'+'tory'='HISTORY'
(Other definitions for history that I've seen before include "The record of past events" , "Chronicle" , "Old record" , "'... repeats itself'" , "eventful past" .)