Not much of a dog? (3)
I believe the answer is:
pom
'dog?' is the definition.
(short for Pomeranian)
I cannot understand how the remainder of the clue works.
Can you help me to learn more?
(Other definitions for pom that I've seen before include "Disparaging term for English immigrants to the Antipodes" , "English person" , "expat Englishman" , "best friend?" , "Small dog (colloq.)" .)