The most common and most likely answer to this crossword clue is the 4 plus 6 letter word CLAY PIGEON
I've seen this crossword clue in The Guardian
C
L
A
Y
P
I
G
E
O
N
More clues leading to the result CLAY PIGEON
- Gone out chasing cases of criminal activity — constant or moving target?
- Ali G follows foreign character, one foolish target
- After endless applause, Daley finally dove into moving target
- .Flying saucer?
- Coping badly with Yale, being object of 8ac 11?
- What may become a hit soon after its release?
- One’s brought down in sport? Bet the swine will come in running once
- Note place and time animal’s caught and used as target
Buddy explains!

The straight part
We know that "moving target" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case moving target = clay pigeon.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.