Dog beat favourite (7)
I believe the answer is:
whippet
'dog' is the definition.
(whippet is a kind of dog)
'beat favourite' is the wordplay.
'beat' becomes 'whip' (whipping is a kind of beating).
'favourite' becomes 'pet' (synonyms).
'whip'+'pet'='WHIPPET'
(Other definitions for whippet that I've seen before include "Greyhound relative" , "dog class?" , "Dog bred for racing" , "Dog related to 9 down" , "Small greyhound-type dog" .)