The most common and most likely answer to this crossword clue is the 9 letter word INITIALED
I've seen this crossword clue in The Guardian
I
N
I
T
I
A
L
E
D
Buddy explains!
The straight part
We know that "Noted agreement" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case noted agreement = initialed.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 INITIALED mean?
INITIALED verb- To sign one's initial(s), as an abbreviated signature.