The most common and most likely answer to this crossword clue is the 7 plus 5 letter word BURNING ISSUE
I've seen this crossword clue in The Times
B
U
R
N
I
N
G
I
S
S
U
E
More clues leading to the result BURNING ISSUE
Buddy explains!

The straight part
We know that "a crucial matter" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a crucial matter = burning issue.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.