Horse-riding competition just ahead of time (5)
I believe the answer is:
event
'horse-riding competition' is the definition.
(I've seen this before)
'just ahead of time' is the wordplay.
'just' becomes 'even'.
'ahead of' is a charade indicator (letters next to each other) (some letters go in front of others).
'time' becomes 't' (abbreviation).
'even'+'t'='EVENT'
(Other definitions for event that I've seen before include "heat, perhaps" , "important" , "Race contest; occasion" , "one item in programme" , "long jump, say" .)