Racecourse favourite giving special welcome (3,6)
I believe the answer is:
red carpet
'special welcome' is the definition.
(special welcome for celebrities)
'racecourse favourite' is the wordplay.
'racecourse' becomes 'redcar' (racecourse in North Yorkshire).
'favourite' becomes 'pet' (synonyms).
'redcar'+'pet'='RED CARPET'
'giving' is the link.
(Other definitions for red carpet that I've seen before include "It is rolled out for VIPs" , "Welcoming ground cover" , "Welcoming walkway" , "for star treatment" , "see VIP on this?" .)