The most common and most likely answer to this crossword clue is the 6 letter word DEMURE
I've seen this crossword clue in The Times
D
E
M
U
R
E
More clues leading to the result DEMURE
- Modest protest over issue's ending
- Before end of sale, object reserved
- Take exception to Egyptian leader retiring
- Raise objection before finally retiring
- Reserved object, English
- Affectedly modest object
- Reserved object, last in sale
- Mild serum Edison keeps around
- Shy Earl follows protest
- . Horribly rude with me? On the contrary
Buddy explains!

The straight part
We know that "Modest" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case modest = demure.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 DEMURE mean?
DEMURE verb- To look demurely.
- (usually of women) Quiet, modest, reserved, sober, or serious.
- Affectedly modest, decorous, or serious; making a show of gravity.