The most common and most likely answer to this crossword clue is the 9 letter word LIQUIDATE
I've seen this crossword clue in The Daily Telegraph
L
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Q
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More clues leading to the result LIQUIDATE
Buddy explains!

The straight part
We know that "Kill" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case kill = liquidate.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.
Crossword Answer definitions
LIQUIDATE verb- To settle (a debt) by paying the outstanding amount.
- To settle the affairs of (a company), by using its assets to pay its debts.
- To convert (assets) into cash; to redeem.
- To determine by agreement or by litigation the precise amount of (indebtedness); to make the amount of (a debt) clear and certain.
- To do away with.
- To kill.
- To make clear and intelligible.
- To make liquid.