The most common and most likely answer to this crossword clue is the 9 letter word OBEDIENCE
I've seen this crossword clue in The Times
O
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More clues leading to the result OBEDIENCE
- Love place to sleep niece arranged in dutifulness
- Old piece of furniture niece destroyed, following instructions
- Previously guards live and die, showing respect
- When guarding base, that is dutiful behaviour
- To follow orders, need ice to melt on 23
- Naughty niece after honour at last redeemed for good behaviour
- As soon as guards happen to fade away, that’s submission
- Respect and honour for princess, hence hatless
- Duty of Bede, I suspect, in ordinary northern church
- Respect at one time shown round base, current base
Buddy explains!

The straight part
We know that "dutifulness" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case dutifulness = obedience.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 OBEDIENCE mean?
OBEDIENCE noun- The quality of being obedient.
- The collective body of persons subject to any particular authority.
- A written instruction from the superior of an order to those under him.
- Any official position under an abbot's jurisdiction.