Woman has dirty laundry (4)
I believe the answer is:
wash
'laundry' is the definition.
('wash' can be a synonym of 'laundry')
'woman has dirty' is the wordplay.
'woman' becomes 'w' (abbreviation eg in Woman Police Constable).
'dirty' is an anagram indicator.
'has' anagrammed gives 'ash'.
'w'+'ash'='WASH'
(Other definitions for wash that I've seen before include "Bear investigation" , "Clean with water" , "Stand up" , "bath" , "Clean oneself" .)