The lady's adopting a bird — big mistake! (6)
I believe the answer is:
howler
'big mistake' is the definition.
'howler' can be an answer for 'mistake' (I have seen 'Serious mistake' mean 'howler' so perhaps 'mistake' could also mean 'howler'). I'm unsure of the 'big' bit.
'the lady's adopting a bird' is the wordplay.
'the lady' becomes 'her' (I've seen this before).
'adopting' indicates putting letters inside.
'a bird' becomes 'owl' (owl is a kind of bird).
'her' enclosing 'owl' is 'HOWLER'.
Can you help me to learn more?
(Other definitions for howler that I've seen before include "Gaffe" , "A glaring mistake, sounds vocally noisy" , "Glaring error" , "Stupid glaring mistake" , "A glaring mistake, perhaps by schoolboy" .)