The most common and most likely answer to this crossword clue is the 4 plus 3 plus 8 letter word PUSH THE ENVELOPE
I've seen this crossword clue in Financial Times
P
U
S
H
T
H
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N
V
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P
E
More clues leading to the result PUSH THE ENVELOPE
Buddy explains!
The straight part
We know that "Through the letter box, postmen may/innovate" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case through the letter box, postmen may/innovate = push the envelope.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.