Pick up cash for fur (3)
I believe the answer is:
doe
'fur' is the definition.
(fur of a female deer)
'pick up cash' is the wordplay.
'pick up' indicates a 'sounds like' (homophone) clue (I've seen 'picked up' mean this).
'cash' becomes 'dough' (dough can informally mean money).
'dough' is a homophone of 'DOE'.
'for' is the link.
(Other definitions for doe that I've seen before include "Last FA Cup winners" , "Mummy rabbit" , "Ode to a female deer" , "possible mate for Rudolph?" , "A female deet" .)