The most common and most likely answer to this crossword clue is the 7 letter word PURSUIT
I've seen this crossword clue in The Daily Telegraph
P
U
R
S
U
I
T
More clues leading to the result PURSUIT
Buddy explains!

The straight part
We know that "Occupation" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case occupation = pursuit.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.
What does PURSUIT mean?
PURSUIT noun- The act of pursuing.
- A hobby or recreational activity, done regularly.
- A discipline in track cycling where two opposing teams start on opposite sides of the track and try to catch their opponents.
- Prosecution