Replenish to give to the little dog (3,2)
I believe the answer is:
top up
'replenish' is the definition.
(I've seen this before)
'give to the little dog' is the wordplay.
'give' is a charade indicator (letters next to each other).
'the little dog' becomes 'pup'.
'to' next to 'pup' is 'TOP-UP'.
'to' acts as a link.
(Other definitions for top up that I've seen before include "Extra amount" , "Serving" , "Give more drink" , "Something extra" , "Give a refill" .)