Fashionable greeting among Conservatives (4)
I believe the answer is:
chic
'fashionable' is the definition.
(chic means stylish or fashionable)
'greeting among conservatives' is the wordplay.
I cannot really understand how this works, but
'greeting' could be 'hi' (hi is a kind of greeting) and 'hi' is found in the answer.
'conservatives' could be 'cc' (an abbreviation for Conservative written twice) and 'cc' is found in the leftover letters.
This accounts for all the letters.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for chic that I've seen before include "French elegance" , "Elegantly fashionable" , "Stylish and elegant - in France" , "Stylishly turned out" , "Fashionably smart" .)