The most common and most likely answer to this crossword clue is the 9 letter word CONNUBIAL
I've seen this crossword clue in The Guardian
C
O
N
N
U
B
I
A
L
Buddy explains!
The straight part
We know that "of matrimony/of matrimony" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case of matrimony/of matrimony = connubial.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 CONNUBIAL mean?
CONNUBIAL adjective- Of or relating to the state of being married.