Perhaps Judy’s young dog, much-liked (6)
I believe the answer is:
puppet
'perhaps judy's' is the definition.
(as in Punch and Judy)
'young dog much-liked' is the wordplay.
'young dog' becomes 'pup' (I've seen this before).
'much-liked' becomes 'pet' (as in a pet project).
'pup'+'pet'='PUPPET'
(Other definitions for puppet that I've seen before include "Small figure of a person operated with strings" , "Toy (with strings attached?)" , "Doll operated by strings" , "Small doll on strings" , "Manipulated figure" .)