The most common and most likely answer to this crossword clue is the 5 plus 7 letter word CAUSE CELEBRE
I've seen this crossword clue in The Daily Telegraph
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More clues leading to the result CAUSE CELEBRE
- Controversy because cereals deficient in arsenic are adulterated
- Sue cereal company’s head and be ruined in famous trial
- Worry about American and European star in noted trial
- Reason with star about famous controversy?
- Reason before church, rebel free to make it a public debate
- About to exploit star concerned with controversial issue
Buddy explains!

The straight part
We know that "famous controversy" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case famous controversy = cause celebre.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.