Dog's "dog” (3)
I believe the answer is:
paw
'dog's dog' is the definition.
(I've seen this in another clue)
This is the entire clue.
(Other definitions for paw that I've seen before include "Hand; foot" , "Animal foot or hill-billy dad" , "Manhandle" , "Eg, a dog's foot" , "Foot of clawed animal" .)