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