The most common and most likely answer to this crossword clue is the 2 plus 2 letter word UP TO
I've seen this crossword clue in Independent
U
P
T
O
More clues leading to the result UP TO
- As far as university, carry on reading
- Put another way, nothing doing
- Doing university? I am not finished yet!
- As much as leaders of United paid trainer Mourinho in the end?
- Capable of two thirds output? That’s dodgy
- So far fit for the job
- Busy at university, getting advice to read more
- Doing no more than …
- Put out – nothing is fit for the job
- Instruction to keep reading university’s first indication of responsibility
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 = up to.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.