The most common and most likely answer to this crossword clue is the 8 letter word MONOGAMY
I've seen this crossword clue in The Times
M
O
N
O
G
A
M
Y
More clues leading to the result MONOGAMY
Buddy explains!

The straight part
We know that "singular marital state" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case singular marital state = monogamy.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 MONOGAMY mean?
MONOGAMY noun- A form of sexual bonding involving a permanent pair bond between two beings.
- The practice of being married to one person as opposed to multiple.