The most common and most likely answer to this crossword clue is the 15 letter word SELF-EFFACEMENT
S
E
L
F
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E
F
F
A
C
E
M
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N
T
Buddy explains!
The straight part
We know that "modesty" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case modesty = self-effacement.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 SELF-EFFACEMENT mean?
SELF-EFFACEMENT noun- The act of keeping oneself in the background, as in humility.