The most common and most likely answer to this crossword clue is the 9 plus 5 letter word COMMUNIST PARTY
I've seen this crossword clue in The Sunday Telegraph
C
O
M
M
U
N
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S
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P
A
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Buddy explains!
The straight part
We know that "his extreme opponents" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case his extreme opponents = communist party.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.