The most common and most likely answer to this crossword clue is the 7 plus 6 letter word PRIVATE SECTOR
I've seen this crossword clue in The Times
P
R
I
V
A
T
E
S
E
C
T
O
R
More clues leading to the result PRIVATE SECTOR
- Government not in control of this soldier faction meeting other ranks
- Soldiers beheaded Achilles’ foe — not state business
- Grunt, adjusting corset — it’s no business of the state!
- Overprices tat that’s flogged where profit’s sought?
- Place for business? Proactive to work with rest
- Soldier escort arranged for individually-owned businesses
- Porters active at work in entrepreneurial area
- Tax in store, price that's bad for part of nation's economy
Buddy explains!
The straight part
We know that "not state business" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case not state business = private sector.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.