I prosecute after second matter (5)
I believe the answer is:
issue
'matter' is the definition.
('issue' can be a synonym of 'matter')
'i prosecute after second' is the wordplay.
'prosecute' becomes 'sue' (I've seen this before).
'after' is a charade indicator (letters next to each other).
'second' becomes 's' (common abbreviation).
'sue' put after 's' is 'ssue'.
'i'+'ssue'='ISSUE'
(Other definitions for issue that I've seen before include "Question that must be settled" , "Children; put out" , "Come forth or bring out" , "something to discuss" , "Bone of contention" .)