Divine messenger initially annoyed woman (6)
I believe the answer is:
angela
'woman' is the definition.
'divine messenger initially annoyed' is the wordplay.
'divine messenger' becomes 'angel' (I've seen this before).
'initially' says to take the initial letters.
The initial letter of 'annoyed' is 'a'.
'angel'+'a'='ANGELA'
(Other definitions for angela that I've seen before include ". . . Lansbury (actress)" , "woman" , "------ Gheorghiu, diva" , "Frau Merkel" , "- Carter, English writer" .)