Housework finished at home, with pig outside (9)
I believe the answer is:
Here is my best explanation:
'housework' is the definition.
'finished at home with pig outside' is the subsidiary indication.
'finished' becomes 'over' ('over' can be similar in meaning to 'finished'**).
'at home' becomes 'in' ('in' can be similar in meaning to 'at home').
'with' is a charade indicator (letters next to each other).
'pig' becomes 'hog' ('hog' can be a synonym of 'pig').
'outside' indicates putting letters inside.
'overin' inserted into 'hog' is 'hoovering'.
(Other definitions for hoovering that I've seen before include "domestic chore", "sucking up" and "Domestic chore".)