Boy having beer cold (4)
I believe the answer is:
alec
'boy' is the definition.
(boy's name)
'beer cold' is the wordplay.
'beer' becomes 'ale' (type of beer).
'cold' becomes 'c' (eg on taps).
'ale'+'c'='ALEC'
'having' is the link.
(Other definitions for alec that I've seen before include "Boy's name (a smart one?)" , "Smart boy?" , "Sir - Douglas-Home, former PM" , "Smart chap" , "A smart . . . . is a know-all in lace" .)