Neglect the old man's drink (4,2)
I believe the answer is:
pass up
'neglect' is the definition.
(thesaurus)
'the old man's drink' is the wordplay.
'the old man's' becomes 'pas' ('pa' can be a synonym of 'old man').
'drink' becomes 'sup' (I've seen this before).
'pas'+'sup'='PASS UP'
(Other definitions for pass up that I've seen before include "col?" , "Neglect (an opportunity)" , "Showing neglect" , "Have nothing to do with" , "Miss" .)