Little time before long trip, missing start for early contest (7)
I believe the answer is:
tourney
'early contest' is the definition.
(historical term for a tournament)
'little time before long trip missing start' is the wordplay.
'little time' becomes 't' (abbreviation for time).
'before' is a charade indicator (letters next to each other).
'long trip' becomes 'journey'.
'missing start' means to remove the first letter.
'journey' with its first letter removed is 'ourney'.
't'+'ourney'='TOURNEY'
'for' is the link.
(Other definitions for tourney that I've seen before include "Competition" , "competitive event" , "US sports event" .)