The race organised nearly doesn't start (5)
I believe the answer is:
relay
'the race' is the definition.
(thesaurus)
'organised nearly doesn't start' is the wordplay.
'organised' is an anagram indicator.
'doesn't start' means to remove the first letter.
'nearly' with its first letter removed is 'early'.
'early' is an anagram of 'RELAY'.
(Other definitions for relay that I've seen before include "Broadcast" , "Receive and pass on - race" , "Pass on - put down again" , "Hand, pass on" , "track event" .)