Woman’s British: Rosemary? (4)
I believe the answer is:
herb
'rosemary?' is the definition.
(rosemary is a kind of herb)
'woman's british' is the wordplay.
'woman' becomes 'her' (pronoun for a woman).
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'her'+'b'='HERB'
(Other definitions for herb that I've seen before include "Parsley, for instance" , "Type of plant used in medicine" , "Maybe sage" , "Wayside plant with small red flowers" , "Marjoram, say" .)