Cryptic crossword clue
Senator grins wickedly about statesman’s first offence 13

The most common and most likely answer to this crossword clue is the 13 letter word TRANSGRESSION

I've seen this crossword clue in The Daily Telegraph
T
R
A
N
S
G
R
E
S
S
I
O
N

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 = transgression.
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 TRANSGRESSION mean?

TRANSGRESSION noun
  1. A violation of a law, duty or commandment.
  2. An act that goes beyond generally accepted boundaries.
  3. A relative rise in sea level resulting in deposition of marine strata over terrestrial strata.

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