Housework finished at home, with pig outside (9)
I believe the answer is:
hoovering
'housework' is the definition.
'finished at home with pig outside' is the wordplay.
'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' means one lot of letters go next to another.
'pig' becomes 'hog' ('hog' can be a synonym of 'pig').
'outside' indicates putting letters inside.
'over'+'in'='overin'
'overin' put inside 'hog' is 'HOOVERING'.
(Other definitions for hoovering that I've seen before include "sucking up" , "Domestic chore" .)