Announced "Oh, I see, chasing that woman is daring" (6)
I believe the answer is:
heroic
'is daring' is the definition.
(thesaurus)
'announced oh i see chasing that woman' is the wordplay.
'announced' shows a homophone (sound like).
'see' becomes 'c' (the word for the letter, according to Chambers).
'chasing' is a charade indicator (letters next to each other).
'that woman' becomes 'her' (I've seen this before**).
'oh' is a homophone of 'o'.
'o'+'i'+'c'='oic'
'oic' put after 'her' is 'HEROIC'.
(Other definitions for heroic that I've seen before include "Showing no fear in the face of extreme difficulty" , "Extravagant" , "Epic" , "Surpassing the ordinary, in courage say" , "Courageous - daring" .)