Fashionable greeting used among Conservatives (4)
I believe the answer is:
chic
'fashionable' is the definition.
(chic means stylish or fashionable)
'greeting used among conservatives' is the wordplay.
I cannot quite 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' (C is an abbreviation for Conservative) and 'cc' is present in the remaining 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 "Smart and stylish, in a French kind of way" , "In vogue" , "Snazzy" , "French elegance" , "Elegant and stylishly fashionable" .)