Woman in Dover argued (4)
I believe the answer is:
vera
'woman' is the definition.
(a woman's name)
'in dover argued' is the wordplay.
'in' indicates a hidden word.
'VERA' is hidden within 'dover argued'.
(Other definitions for vera that I've seen before include ".. Lynn, aloe ..." , "senior songstress?" , "Dame -- Lynn, singer" , "__ Lynn, the forces' sweetheart" , "A girl to rave about" .)