Killer’s success with staff (3,3)
I believe the answer is:
hit man
'killer's' is the definition.
(hit man is a kind of killer)
'success with staff' is the wordplay.
'success' becomes 'hit' (hit is a kind of success).
'with' is a charade indicator (letters next to each other).
'staff' becomes 'man' (manning is a kind of staffing).
'hit'+'man'='HIT-MAN'
(Other definitions for hit man that I've seen before include "A modern paid assassin" , "In slang, a hired assassin" , "One killing" , "Hired killer" , "Hired murderer" .)