Be up for wrongdoing (4)
I believe the answer is:
evil
'for wrongdoing' is the definition.
(evil is a kind of wrongdoing)
'be up' is the wordplay.
'be' becomes 'live' (to be is to live or exist).
'up' is a reversal indicator (in down clue: letters go upwards).
'live' back-to-front is 'EVIL'.
(Other definitions for evil that I've seen before include "Morally bad" , "Profoundly wicked" , "Extremely unpleasant" , "Vile (anag) -- really bad" , "Depraved" .)