False promises disheartened party supporting European Union (6)
I believe the answer is:
pseudo
'false' is the definition.
(I've seen this in another clue)
'promises disheartened party supporting european union' is the wordplay.
'disheartened' suggests removing the centre.
'party' becomes 'do' (do is a kind of party).
'supporting' says to put letters next to each other (in a down clue, some letters go below others).
'european union' becomes 'eu'.
'promises' with its middle removed is 'ps'.
'do' after 'eu' is 'eudo'.
'ps'+'eudo'='PSEUDO'
(Other definitions for pseudo that I've seen before include "Dose up (anag.); pretentious" , "Insincere person" , "Ersatz" , "Not genuine" , "Spurious" .)