Affected a stylish greeting (6)
I believe the answer is:
chichi
'affected' is the definition.
(I've seen this before)
'a stylish greeting' is the wordplay.
'a stylish' becomes 'chic' (I've seen this before).
'greeting' becomes 'hi' (hi is a kind of greeting).
'chic'+'hi'='CHICHI'
(Other definitions for chichi that I've seen before include "Very smart and sophisticated" , "self-consciously stylish" , "3[AFFECTATION]?" , "Very chic, repetitively" , "Affectedly trendy" .)