Party member has short display about deserter (8)
I believe the answer is:
democrat
'party member' is the definition.
(I've seen this in another clue)
'short display about deserter' is the wordplay.
'short display' becomes 'demo' (I can't explain this - if you can you should give a lot more credence to this answer).
'about' becomes 'c' (abbreviation for 'circa').
'deserter' becomes 'rat' (both can mean a traitor).
'demo'+'c'+'rat'='DEMOCRAT'
'has' acts as a link.
Can you help me to learn more?
(Other definitions for democrat that I've seen before include "Cleveland?" , "One who believes in government by the whole people" , "Member of one of US parties" , "One advocates government by the people's elected representatives" , "US political party supporter" .)