The most common and most likely answer to this crossword clue is the 7 plus 1 plus 2 letter word HANGMAN - DD
I've seen this crossword clue in The Times
H
A
N
G
M
A
N
-
D
D
Buddy explains!
The straight part
We know that "Game/official suspending offenders" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case game/official suspending offenders = hangman - dd.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.