The most common and most likely answer to this crossword clue is the 7 plus 2 letter word VATICAN II
I've seen this crossword clue in The Times
V
A
T
I
C
A
N
I
I
Buddy explains!
The straight part
We know that "Council" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case council = vatican ii.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.