Bat at all times suppresses onset of violent gangster (9)
I believe the answer is:
racketeer
'gangster' is the definition.
(thesaurus)
'bat at all times' is the wordplay.
'bat' becomes 'racket' (I've seen this before).
'at all times' becomes 'eer' (archaic or poetic word meaning ever or forever).
'racket'+'eer'='RACKETEER'
'suppresses onset of violent' is the link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for racketeer that I've seen before include "Mafia-type" , "Fraudulent dealer" , "Crook" , "Wide boy" , "Fraudulent businessman" .)