Exile elected to office rising in party (6)
I believe the answer is:
banish
'exile' is the definition.
(I've seen this before)
'rising in party' is the wordplay.
'rising' becomes 'ni' (I can't justify this - if you can you should give a lot more credence to this answer).
'in' indicates putting letters inside.
'party' becomes 'bash' (term for a party or celebration).
'ni' going within 'bash' is 'BANISH'.
'elected to office' acts as a link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for banish that I've seen before include "dislodge" , "outlaw" , "Condemn to exile" , "Exile in ash-bin" , "Throw out" .)