The most common and most likely answer to this crossword clue is the 4 letter word PRIM
I've seen this crossword clue in The Guardian
P
R
I
M
More clues leading to the result PRIM
- Page, reserved initially, I am finding formal
- Chief, endlessly formal
- Strait-laced Puritan leader outside
- Fastidious setter’s following promising leads
- Parking by the verge is proper
- Quiet, on edge and rather demure
- Fifth off 2 or 3 perhaps, to be formal
- Overly formal chief cut short
- Penny’s on edge, being prudish
- Punctilious Trojan king has no answer
Buddy explains!
The straight part
We know that "rather demure" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case rather demure = prim.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 PRIM mean?
PRIM verb- To make affectedly precise or proper.
- To dress or act smartly.
- Prudish, straight-laced
- Formal; precise; affectedly neat or nice
- (plants) privet