Not the first time (6)
I believe the answer is:
second
I believe this clue is a double definition.
'not the first' is the first definition.
(not the first but the second)
'time' is the second definition.
(unit of time)
(Other definitions for second that I've seen before include "Position of runner-up" , "Further opportunity" , "A duellist's or boxer's assistant" , "Assistant in the ring" , "Support - a little time" .)