The most common and most likely answer to this crossword clue is the 6 letter word SINNER
I've seen this crossword clue in The Daily Telegraph
S
I
N
N
E
R
Buddy explains!

The straight part
We know that "Offender" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case offender = sinner.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 SINNER mean?
SINNER noun- A person who sins or has sinned.
- A person who sins or has sinned by the action or identity indicated or previously mentioned
- An unregenerate person.
- (figuratively, by extension) A person with negative qualities; one who does bad things.