Quickly running past those (9)
I believe the answer is:
posthaste
'quickly' is the definition.
(thesaurus)
'running past those' is the wordplay.
'running' is an anagram indicator.
'past'+'those'='pastthose'
'pastthose' with letters rearranged gives 'POSTHASTE'.
(Other definitions for posthaste that I've seen before include "With particular speed" , "With great speed and urgency" , "With utmost speed -- to the pass (anag)" , "As quickly as possible" , "Like Bat out of Hell" .)