Go wrong with delivery run (6)
I believe the answer is:
errand
'delivery run' is the definition.
'go wrong with' is the wordplay.
'go wrong' becomes 'err' (I've seen this before).
'with' becomes 'and' (I've seen this before).
'err'+'and'='ERRAND'
(Other definitions for errand that I've seen before include "Short delivery journey" , "Journey made on someone else's behalf" , "light task" , "Trip for small task" , "Short trip with a mission" .)