The most common and most likely answer to this crossword clue is the 10 letter word TWENTIETHS
I've seen this crossword clue in The Times
T
W
E
N
T
I
E
T
H
S
Buddy explains!

The straight part
We know that "Parts of China party" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case parts of china party = twentieths.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 TWENTIETHS mean?
TWENTIETHS noun- A person or thing in the twentieth position.
- One of twenty equal parts of a whole.