Caught out, protest against race for connoisseur’s piece (5,4)
I believe the answer is:
objet dart
'connoisseur's piece' is the definition.
(an art connoisseur might own an objet d'art)
'caught out protest against race' is the wordplay.
'caught' becomes 'c' (cricket abbreviation).
'out' suggests deleting specific letters.
'protest against' becomes 'object'.
'race' becomes 'dart' (darting is a kind of racing**).
'object' with 'c' removed is 'objet'.
'objet'+'dart'='OBJET DART'
'for' acts as a link.
(Other definitions for objet dart that I've seen before include "something treasured" , "curiosity" , "Collector's piece (5,1'3)" , "Decorative item" , "Exquisite piece" .)