Aussie bird without dress recalled offence (7)
I believe the answer is:
umbrage
'offence' is the definition.
(I know that offence can be written as umbrage)
'aussie bird without dress recalled' is the wordplay.
'aussie bird' becomes 'emu' (I've seen this before).
'without' means one lot of letters goes inside another ('without' can be similar in meaning to 'outside').
'dress' becomes 'garb' (synonyms).
'recalled' says the letters should be written in reverse.
'emu' going around 'garb' is 'egarbmu'.
'egarbmu' backwards is 'UMBRAGE'.
(Other definitions for umbrage that I've seen before include "Suspicion of injury" , "Take this to be offended" , "Take this to show offence" , "Offence that's usually taken" , "In high dudgeon" .)