The most common and most likely answer to this crossword clue is the 11 letter word INTERROGATE
I've seen this crossword clue in The Daily Telegraph
I
N
T
E
R
R
O
G
A
T
E
More clues leading to the result INTERROGATE
Buddy explains!

The straight part
We know that "Question" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case question = interrogate.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 INTERROGATE mean?
INTERROGATE verb- To question or quiz, especially in a thorough and/or aggressive manner
- To query; to request information from.
- To examine critically.