The most common and most likely answer to this crossword clue is the 11 letter word INVESTIGATE
I've seen this crossword clue in The Daily Telegraph
I
N
V
E
S
T
I
G
A
T
E
More clues leading to the result INVESTIGATE
- Wearing top I keep in school study
- Make inquiries about it, seeing a TV broadcast
- Consider wearing underwear? One reaches a scandalous conclusion
- Spy, possibly shirtless, faces international ‘scandal’
- Search is prompt checking vehicle’s exterior
- Having put on underwear, I exit and check out
- Lay out one on door search
- Consider perhaps shirtless soldier upped and bolted
- I’ve a testing break down to do this
- Given a test, I organised research
Buddy explains!

The straight part
We know that "search" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case search = investigate.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 INVESTIGATE mean?
INVESTIGATE verb- To inquire into or study in order to ascertain facts or information.
- To examine, look into, or scrutinize in order to discover something hidden or secret.
- To conduct an inquiry or examination.