Brave, head off a mad woman (4)
I believe the answer is:
vera
'woman' is the definition.
(a woman's name)
'brave head off a mad' is the wordplay.
'head off' means to remove the first letter.
'a mad' indicates an anagram.
'brave' with its first letter taken away is 'rave'.
'rave' anagrammed gives 'VERA'.
(Other definitions for vera that I've seen before include ".. Lynn, aloe ..." , "__ Lynn, the forces' sweetheart" , "Duckworth, Lynn" , "senior songstress?" , "Girl's name (meaning faith or true)" .)