Punishment causes acne to break out (4)
I believe the answer is:
cane
'punishment' is the definition.
(I've seen this in other clues)
'acne to break out' is the wordplay.
'to break out' is an anagram indicator.
'acne' with letters rearranged gives 'CANE'.
'causes' is the link.
(Other definitions for cane that I've seen before include "Walking stick; punish" , "Malacca, perhaps" , "Kind of sugar?" , "A light rod once used for punishment" , "African country formerly called Gold Coast" .)