Hard right-winger supporting one's record (7)
I believe the answer is:
history
'record' is the definition.
(history is a kind of record)
'hard right-winger supporting one's' is the wordplay.
'hard' becomes 'h'.
'right-winger' becomes 'tory' (Tory is an example).
'supporting' is a charade indicator (letters next to each other) (in a down clue, some letters go below others).
'one's' becomes 'is' (roman numeral).
'tory' put after 'is' is 'istory'.
'h'+'istory'='HISTORY'
(Other definitions for history that I've seen before include "'... repeats itself'" , "Life story" , "Background" , "Account of past events" , "Chronicle" .)