The most common and most likely answer to this crossword clue is the 2 plus 4 letter word AT WORK
I've seen this crossword clue in The Guardian
A
T
W
O
R
K
More clues leading to the result AT WORK
Buddy explains!

The straight part
We know that "Busy" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case busy = at work.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.