Drunk next to bar - that's sweet (5,4)
I believe the answer is:
tipsy cake
'sweet' is the definition.
(tipsy cake is a kind of sweet)
'drunk next to bar' is the wordplay.
'drunk' becomes 'tipsy' (tipsy means somewhat drunk).
'next to' says to put letters next to each other.
'bar' becomes 'cake' (synonyms).
'tipsy'+'cake'='TIPSY-CAKE'
'that's' is the link.
(Other definitions for tipsy cake that I've seen before include "Dessert of pastry, almonds and wine" , "Trifle with white wine or sherry" , "Pudding" , "Trifle with alcohol, almonds and crystallised fruit" , "Dessert of sponge soaked with wine or spirits" .)