Is inclined to go after success — lots available to offers? (3,5)
I believe the answer is:
hit lists
'lots available to offers?' is the definition.
(an assassin is someone who 'offs' people)
'is inclined to go after success' is the wordplay.
'is inclined' becomes 'lists' (list can mean to lean or tip over).
'to go after' means one lot of letters go next to another.
'success' becomes 'hit' (hit is a kind of success).
'lists' after 'hit' is 'HIT LISTS'.
(Other definitions for hit lists that I've seen before include "Table of names of those to be killed" , "People may be killed on these" .)