The most common and most likely answer to this crossword clue is the 3 letter word COY
I've seen this crossword clue in The Daily Telegraph
C
O
Y
More clues leading to the result COY
Buddy explains!

The straight part
We know that "Demure" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case demure = coy.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 COY mean?
COY verb- To caress, pet; to coax, entice.
- To calm or soothe.
- To allure; to decoy.
- Bashful, shy, retiring.
- Quiet, reserved, modest.
- Reluctant to give details about something sensitive; notably prudish.
- Pretending shyness or modesty, especially in an insincere or flirtatious way.
- Soft, gentle, hesitating.
- A trap from which waterfowl may be hunted.
- A company