The most common and most likely answer to this crossword clue is the 7 plus 4 letter word EMPEROR MOTH
I've seen this crossword clue in The Guardian
E
M
P
E
R
O
R
M
O
T
H
Buddy explains!
The straight part
We know that "Fly-by-night" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fly-by-night = emperor moth.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.