Around home see floor covering (4)
I believe the answer is:
lino
'floor covering' is the definition.
(short for linoleum)
'around home see' is the wordplay.
'around' means one lot of letters goes inside another.
'home' becomes 'in' ('he's home' can mean 'he's in').
'see' becomes 'lo' (archaic word meaning 'look!').
'in' put inside 'lo' is 'LINO'.
(Other definitions for lino that I've seen before include "Floor covering (abbr)" , "'Floor covering, in short (4)'" , "put this down?" , "Tough floor covering" .)