Bit of unfinished business (8)
'bit of unfinished business' is the definition.
(I've seen this in another clue)
This is the entire clue.
(Other definitions for loose end that I've seen before include "Unsettled matter" , "As yet unexplained detail" , "unfinished work" , "'A detail not settled or explained (5,3)'" , "should have been tied?" .)