That woman leave quietly before ground squirrel? (6)
I believe the answer is:
gopher
'ground squirrel?' is the definition.
(I know that ground squirrel can be written as gopher)
'that woman leave quietly before' is the wordplay.
'that woman' becomes 'her' (her refers to a woman).
'leave' becomes 'go'.
'quietly' becomes 'p' (p for piano and quiet).
'before' says to put letters next to each other.
'go'+'p'='gop'
'her' put after 'gop' is 'GOPHER'.
(Other definitions for gopher that I've seen before include "American burrowing rodent or ground squirrel" , "Burrowing rodent of north and central America" , "Rodent - wood of Noah's Ark" , "Method of teaching reading by sounds" , "Burrowing rodent with cheek pouches" .)