The most common and most likely answer to this crossword clue is the 7 letter word BASHFUL
I've seen this crossword clue in The Guardian
B
A
S
H
F
U
L
More clues leading to the result BASHFUL
- One shy of 7
- Party female, university learner looking embarrassed
- Dwarf who’s up for a fight?
- Modest bachelor, somewhat shy, wants female with fabulous heart
- One shy of seven?
- Go to university — oddly, full houses reserved
- One in seven workers is retiring
- Party almost packed for one among celebrated seven
- Shovel and pick worker‘s reserved
- One in seven miners is retiring
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 = bashful.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 BASHFUL mean?
BASHFUL adjective- Shy; not liking to be noticed; socially timid.
- Indicating bashfulness.