Cryptic crossword clue
Among email letters being exchanged, a chronic lack of modesty 11

The most common and most likely answer to this crossword clue is the 11 letter word MEGALOMANIA

I've seen this crossword clue in The Sunday Telegraph
M
E
G
A
L
O
M
A
N
I
A

Buddy explains!

The straight part
We know that "a chronic lack of modesty" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a chronic lack of modesty = megalomania.
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 MEGALOMANIA mean?

MEGALOMANIA noun
  1. A psychopathological condition characterized by delusional fantasies of wealth, power, or omnipotence.
  2. Narcissistic personality disorder.
  3. An obsession with grandiose or extravagant things or actions.

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