Release objective for unfinished business (5,3)
I believe the answer is:
loose end
'unfinished business' is the definition.
('loose end' can be a synonym of 'unfinished business')
'release objective' is the wordplay.
'release' becomes 'loose' (loosing is a kind of releasing).
'objective' becomes 'end' (I've seen this before).
'loose'+'end'='LOOSE END'
'for' acts as a link.
(Other definitions for loose end that I've seen before include "As yet unexplained detail" , "should have been tied?" , "The bored, idle at one" , "unfinished work" , "'A detail not settled or explained (5,3)'" .)