The most common and most likely answer to this crossword clue is the 7 letter word LARCENY
I've seen this crossword clue in The Daily Telegraph
L
A
R
C
E
N
Y
More clues leading to the result LARCENY
- Criminal activity surprisingly clear and near once
- Crime nearly sorted out: Charlie's collared
- Clear criminal linked to New York theft
- Clear criminal over US city crime
- Crime nearly out of control around Cuba
- Conservative nearly reformed? That’s wrong
- Distracted, nearly caught thieving
- Crime nearly solved after drug seized
- Clear out American city’s petty crime
- Regularly seen wearing Lycra — possibly an offence!
Buddy explains!

The straight part
We know that "an offence" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case an offence = larceny.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 LARCENY mean?
LARCENY noun- The unlawful taking of personal property as an attempt to deprive the legal owner of it permanently.
- A larcenous act attributable to an individual.