Pet fur has nothing removed (3)
I believe the answer is:
cat
This clue might be a double definition.
'pet' is the first definition.
(cats are often kept as pets)
'fur has nothing removed' is the second definition.
I know that 'fur' relates to this answer.
(Other definitions for cat that I've seen before include "Feline - whip" , "Sailor's whip with nine knotted strands" , "Feline mammel" , "one's pyjamas? They're an excellent thing" , "eg Leopard" .)