An outrageous act or getting into hostility (8)
I believe the answer is:
enormity
'an outrageous act' is the definition.
(I've seen this in another clue)
'or getting into hostility' is the wordplay.
'getting into' means one lot of letters goes inside another.
'hostility' becomes 'enmity' (synonyms).
'or' going inside 'enmity' is 'ENORMITY'.
(Other definitions for enormity that I've seen before include "Great wickedness - more tiny (anag)" , "Shocking act" , "act of wickedness?" , "Grave crime or sin" , "Outrage" .)