The most common and most likely answer to this crossword clue is the 8 letter word POLYGAMY
I've seen this crossword clue in The Daily Telegraph
P
O
L
Y
G
A
M
Y
Buddy explains!

The straight part
We know that "Offence" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case offence = polygamy.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 POLYGAMY mean?
POLYGAMY noun- The condition of having more than one spouse or marriage partner at one time.
- The state or habit of having more than one sexual mate.
- The condition or state of a plant which bears both perfect and unisexual flowers.
- The state or practice of having several wives at the same time; plurality of wives; marriage to several wives.
- The condition of an ant colony that has multiple egg-laying queens.