Fall behind with hesitancy, due to drink (5)
I believe the answer is:
lager
'to drink' is the definition.
(lager is a kind of drink)
'fall behind with hesitancy due' is the wordplay.
'fall behind' becomes 'lag' (synonyms).
'with' is a charade indicator (letters next to each other).
'hesitancy due' becomes 'er' (I am not sure about this - if you are sure you should believe this answer much more).
'lag'+'er'='LAGER'
Can you help me to learn more?
(Other definitions for lager that I've seen before include "Tipple" , "Light-coloured beer" , "The drink could be regal" , "Regal sort of beer" , "Light beer; sounds like camp" .)