The most common and most likely answer to this crossword clue is the 6 plus 6 letter word POSTAL BALLOT
I've seen this crossword clue in The Times
P
O
S
T
A
L
B
A
L
L
O
T
More clues leading to the result POSTAL BALLOT
Buddy explains!
The straight part
We know that "Vote that's put in a box" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case vote that's put in a box = postal ballot.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.