The most common and most likely answer to this crossword clue is the 6 plus 5 letter word SECRET AGENT
I've seen this crossword clue in The Daily Telegraph
S
E
C
R
E
T
A
G
E
N
T
More clues leading to the result SECRET AGENT
- Bond maybe broken centre stage
- Spy that’s centre stage, strangely
- Stupidly put secret agent in most prominent position
- Spy dispatched, having collected odd bits of gear etc
- Spook seaman going round most of island
- Man of intelligence moves centre stage
- It would be unusual for this spy to be centre stage
- Spy’s target seen moving round about
- Most of islander information snatched by determined spy
- Bum steer can get someone involved in espionage
Buddy explains!

The straight part
We know that "It would be unusual for this spy to be centre stage" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case it would be unusual for this spy to be centre stage = secret agent.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.