The most common and most likely answer to this crossword clue is the 7 letter word BOTTLED
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Buddy explains!

The straight part
We know that "Kept" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case kept = bottled.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 BOTTLED mean?
BOTTLED verb- To seal (a liquid) into a bottle for later consumption. Also fig.
- To feed (an infant) baby formula.
- To refrain from doing (something) at the last moment because of a sudden loss of courage.
- To throw away a leading position.
- To strike (someone) with a bottle.
- To pelt (a musical act on stage, etc.) with bottles as a sign of disapproval.
- Packaged in a bottle.
- Drunk
- Shaped or protuberant like a bottle.
- Kept in restraint; bottled up.