Half a woolly ball for little dog (3)
I believe the answer is:
pom
'little dog' is the definition.
(Pom is short for Pomeranian)
'half a woolly ball' is the wordplay.
'half a' indicates taking half.
'woolly ball' becomes 'pompom' (I've seen this before).
'pompom' halved is 'POM'.
'for' is the link.
(Other definitions for pom that I've seen before include "Little dog" , "English person" , "Shortened name for a breed of dog" , "Limey in Oz" , "Australian slang for British migrant" .)