The vet yearned to reform equestrian contest (5-3,5)
I believe the answer is:
three-day event
'equestrian contest' is the definition.
'the vet yearned to reform' is the wordplay.
'to reform' indicates an anagram.
'the'+'vet'+'yearned'='thevetyearned'
'thevetyearned' with letters rearranged gives 'THREE-DAY EVENT'.
(Other definitions for three-day event that I've seen before include "Horse-riding competition" , "Equestrian competition involving several skills" , "Equestrian competition comprising several disciplines" , "Dressage, cross-country and showjumping" .)