Tear a strip off floor covering (6)
I believe the answer is:
carpet
I believe this is a double definition.
'tear a strip off' is the first definition.
(I've seen this before)
'floor covering' is the second definition.
(carpet is a kind of floor covering)
(Other definitions for carpet that I've seen before include "roll of fabric?" , "Flooring fabric" , "Be on this floor covering to be reprimanded" , "It could be flying" , "Floor cover" .)