Buy son (not Oscar) a little dog (4,2)
I believe the answer is:
snap up
'buy' is the definition.
(to snap something up is to buy it quickly)
'son not oscar a little dog' is the wordplay.
'not' suggests deleting specific letters.
'oscar' becomes 'O' (phonetic alphabet: alpha, bravo, charlie etc.).
'little dog' becomes 'pup' (short for puppy).
'son' with 'o' taken out is 'sn'.
'sn'+'a'+'pup'='SNAP UP'
(Other definitions for snap up that I've seen before include "Snatch" , "Unhesitatingly take" , "Quickly accept" , "Grab eagerly and quickly" , "Buy (a rarity) quickly" .)