Censor woman with no husband (4)
I believe the answer is:
edit
'censor' is the definition.
(censoring is editing out certain content)
'woman with no husband' is the wordplay.
'woman' becomes 'Edith' (woman's name).
'with no' indicates named letters should be taken away.
'husband' becomes 'h'.
'edith' with 'h' removed is 'EDIT'.
(Other definitions for edit that I've seen before include "Manage a newspaper" , "Make alterations (in text)" , "Prepare (material) for publication" , "Tide (anag.)" , "Ready for publication" .)