Support little dog going after professional (4,2)
I believe the answer is:
prop up
'support' is the definition.
(propping up is a kind of supporting)
'little dog going after professional' is the wordplay.
'little dog' becomes 'pup'.
'going after' is a charade indicator (letters next to each other).
'professional' becomes 'pro' (synonyms).
'pup' put after 'pro' is 'PROP UP'.
(Other definitions for prop up that I've seen before include "Underpin" , "Give financial backing" , "Support" , "Keep going" .)