The most common and most likely answer to this crossword clue is the 10 letter word CONSENSUAL
I've seen this crossword clue in The Times
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Buddy explains!
The straight part
We know that "by agreement" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case by agreement = consensual.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 CONSENSUAL mean?
CONSENSUAL adjective- With permission, with consensus, without coercion; allowed without objecting or resisting
- Existing, or made, by the mutual consent of two or more parties
- Excited or caused by sensation, sympathy, or reflex action, and not by conscious volition