Finishes off duck hidden by person in party to eat later on (4,2)

'finishes off' is the definition.
('mop up' can be a synonym of 'finish off')

'duck hidden by person in party to eat later on' is the wordplay.
'duck' becomes 'o' (resembles zero - 'duck' in cricket).
'hidden by' indicates putting letters inside (inserted letters are hidden inside).
'person in party' becomes 'MP' (Member of Parliament, member of a political party).
'to eat' becomes 'sup' (supping is a kind of eating).
'later on' is a charade indicator (letters next to each other) (some letters appear later than others).
'o' placed into 'mp' is 'mop'.
'mop'+'sup'='MOPS UP'