The most common and most likely answer to this crossword clue is the 7 letter word COYNESS
C
O
Y
N
E
S
S
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 = coyness.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 COYNESS mean?
COYNESS noun- The property of being coy.