Contemptuously smile back after first greeting the party (6)
I believe the answer is:
greens
'party' is the definition.
(the Green Party is a political party)
'contemptuously smile back' is the wordplay.
'contemptuously' becomes 'g' (I can't justify this - if you can you should believe this answer much more).
'smile' becomes 'sneer' (sneering is a kind of smiling).
'back' is a reversal indicator.
'sneer' back-to-front is 'reens'.
'g'+'reens'='GREENS'
'after first greeting the' acts as a link.
This may not be right. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for greens that I've seen before include "Nature lovers" , "Cabbage, sprouts etc" , "Ecology party" , "Places for bowling" , "party politicians" .)