The most common and most likely answer to this crossword clue is the 9 letter word CHINAWARE
I've seen this crossword clue in Financial Times
C
H
I
N
A
W
A
R
E
More clues leading to the result CHINAWARE
- Face piece, knowing pottery
- Part of the face: mindful that's fragile
- Tea put round in mostly warm English porcelain
- Where one bravely takes misfortune, conscious it may provide a service
- Feature sensible dinner service
- Facial feature to be conscious of in crockery
- Fragile thing hit, fully conscious
- Pottery feature in the picture
- Arachne messes with WI’s crockery
- A new chair put out — it’s for the dining table
Buddy explains!

The straight part
We know that "Pottery" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case pottery = chinaware.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.