The most common and most likely answer to this crossword clue is the 13 letter word DRINK-DRIVING
I've seen this crossword clue in The Times
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Buddy explains!

The straight part
We know that "Lawbreaking" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case lawbreaking = drink-driving.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 DRINK-DRIVING mean?
DRINK-DRIVING noun- Operation of a motor vehicle after recently consuming an alcoholic beverage.
- A criminal offence committed by a person who operates a vehicle when the measured amount of alcohol in his or her blood exceeds the legal limit.