The most common and most likely answer to this crossword clue is the 9 plus 1 letter word ENORMITY} :
I've seen this crossword clue in The Daily Telegraph
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Buddy explains!
The straight part
We know that "A great crime" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a great crime = enormity} :.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 ENORMITY} : mean?
ENORMITY} : noun- Deviation from what is normal or standard; irregularity, abnormality.
- Deviation from moral normality; extreme wickedness, nefariousness, or cruelty.
- A breach of law or morality; a transgression, an act of evil or wickedness.
- Great size; enormousness, hugeness, immenseness.