Foreign character has a record laugh (5)
I believe the answer is:
alpha
'foreign character' is the definition.
(letter of the Greek alphabet)
'a record laugh' is the wordplay.
'record' becomes 'L-P' (abbreviation for long play record).
'laugh' becomes 'ha'.
'a'+'lp'+'ha'='ALPHA'
'has' acts as a link.
(Other definitions for alpha that I've seen before include "First letter of the Greek alphabet" , "Top grade" , "Foreign character" , "high mark" , "Top star" .)