The most common and most likely answer to this crossword clue is the 7 letter word JEALOUS
I've seen this crossword clue in Financial Times
J
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A
L
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More clues leading to the result JEALOUS
Buddy explains!

The straight part
We know that "green" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case green = jealous.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 JEALOUS mean?
JEALOUS adjective- Suspecting rivalry in love; troubled by worries that one might have been replaced in someone's affections; suspicious of a lover's or spouse's fidelity.
- Protective, zealously guarding, careful in the protection of something one has or appreciates.
- Envious; feeling resentful or angered toward someone for a perceived advantage or success, material or otherwise.
- Suspecting, suspicious.