The most common and most likely answer to this crossword clue is the 4 plus 4 letter word SINN FEIN
I've seen this crossword clue in The Times
S
I
N
N
F
E
I
N
More clues leading to the result SINN FEIN
Buddy explains!

The straight part
We know that "party" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case party = sinn fein.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.