Fleeing (6,2,4,5)
I think it could be either:
taking to ones heels
'fleeing' is the definition.
(I've seen this before)
This is all the clue.
(Other definitions for on the run that I've seen before include "In flight as from the police" , "wanted by the police" , "Fugitive - escaping from arrest" , "Trying to avoid capture" , "Like fugitives" .)