Encourage with, say, have half a flagon (3,2)
I believe the answer is:
egg on
'encourage' is the definition.
(to egg somebody on is to encourage them)
'say have half a flagon' is the wordplay.
'say' becomes 'eg' (both can mean 'for example').
'have' is a charade indicator (letters next to each other).
'half a' means to take half the letters.
'flagon' with half the letters taken is 'gon'.
'eg'+'gon'='EGG ON'
'with' is the link.
(Other definitions for egg on that I've seen before include "Prod" , "Press" , "Urge (someone) to take risks" , "Push" , "Encourage to act" .)