Pole out for a run (4)
I believe the answer is:
lope
'a run' is the definition.
(lope is a kind of run)
'pole out' is the wordplay.
'out' indicates anagramming the letters (out can mean wrong or inaccurate).
'pole' with letters rearranged gives 'LOPE'.
'for' is the link.
(Other definitions for lope that I've seen before include "Slow pace" , "Go with bounding strides" , "Run slowly with pole" , "Bound along carrying pole" , "Canter" .)