The most common and most likely answer to this crossword clue is the 9 letter word PUNCHBOWL
I've seen this crossword clue in The Guardian
P
U
N
C
H
B
O
W
L
More clues leading to the result PUNCHBOWL
Buddy explains!

The straight part
We know that "party kit" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case party kit = punchbowl.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.
What does PUNCHBOWL mean?
PUNCHBOWL noun- A large bowl used for making or serving punch (the beverage).