I agree the woman has caught a flightless bird (4,4)
I believe the answer is:
hear hear
'i agree' is the definition.
(I've seen this before)
'the woman has caught a flightless bird' is the wordplay.
'the woman' becomes 'her'.
'has caught' means one lot of letters goes inside another.
'flightless bird' becomes 'rhea' (rhea is a kind of flightless bird).
'a'+'rhea'='arhea'
'her' enclosing 'arhea' is 'HEAR HEAR'.
(Other definitions for hear hear that I've seen before include "exclaiming repeatedly" , "sound supportive" , "That's right" , "Listen, listen - that's applause!" , "Jolly good!" .)