The most common and most likely answer to this crossword clue is the 9 letter word CHALLENGE
I've seen this crossword clue in The Daily Telegraph
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More clues leading to the result CHALLENGE
- Confront Helen, a GLC eccentric
- Tax measure brought back, cutting a little money
- Take on chief leading all-English league at last
- Check claim involving northern dispute
- Question engineer by vestibule in church
- Object to sentry’s demand for ID
- Question about husband with name in claim
- Object to transformation including east end of Marseille
- Test space craft with no tail
- French town with six missing blocks alteration of summons
Buddy explains!

The straight part
We know that "Take exception to/question" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case take exception to/question = challenge.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 CHALLENGE mean?
CHALLENGE noun- A confrontation; a dare.
- A difficult task, especially one that the person making the attempt finds more enjoyable because of that difficulty.
- A procedure or action.
- The opening and crying of hounds at first finding the scent of their game.
- To invite (someone) to take part in a competition.
- To dare (someone).
- To dispute (something).
- To make a formal objection to a juror.
- To claim as due; to demand as a right.
- To censure; to blame.
- To question or demand the countersign from (one who attempts to pass the lines).
- To object to the reception of the vote of, e.g. on the ground that the person is not qualified as a voter.
- To take (a final exam) in order to get credit for a course without taking it.