The most common and most likely answer to this crossword clue is the 4 plus 1 plus 6 plus 4 letter word LEAD A DOUBLE LIFE
I've seen this crossword clue in The Times
L
E
A
D
A
D
O
U
B
L
E
L
I
F
E
More clues leading to the result LEAD A DOUBLE LIFE
Buddy explains!

The straight part
We know that "moonlight?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case moonlight? = lead a double life.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.