Old thief's put off, breaking into profanity (8)
I believe the answer is:
cutpurse
'old thief's' is the definition.
(old term for a thief)
'put off breaking into profanity' is the wordplay.
'off' indicates anagramming the letters.
'breaking into' is an insertion indicator.
'profanity' becomes 'curse' (curse is a kind of profanity).
'put' with letters rearranged gives 'tpu'.
'tpu' going into 'curse' is 'CUTPURSE'.
(Other definitions for cutpurse that I've seen before include "thief (not me!)" , "Old pickpocket - true cups (anag)" , "Pickpocket -- set up cru (anag)" , "Pickpocket of olden times" , "robber" .)