Rest, stirring before morning run (6)
I believe the answer is:
stream
'run' is the definition.
(I know that stream is a type of run)
'rest stirring before morning' is the wordplay.
'stirring' indicates anagramming the letters.
'before' says to put letters next to each other.
'morning' becomes 'am' (as in 12:00 AM).
'rest' is an anagram of 'stre'.
'stre'+'am'='STREAM'
(Other definitions for stream that I've seen before include "Flow of water on land" , "not taken in mixed-ability group" , "Small watercourse" , "Small narrow flow" , "Master (anag) - current" .)