Quiet chap serving alcoholic drink (6)
I believe the answer is:
shandy
'alcoholic drink' is the definition.
(shandy is an alcoholic drink)
'quiet chap' is the wordplay.
'quiet' becomes 'sh' ('sh' is used to tell someone to be quiet).
'chap' becomes 'andy' (man's name).
'sh'+'andy'='SHANDY'
'serving' is the link.
(Other definitions for shandy that I've seen before include "mixed drink" , "A misture of ale and lemonade" , "Weakly-alcoholic drink" , "Drink made of beer and lemonade" , "Drink of ale and lemonade 96)" .)