The most common and most likely answer to this crossword clue is the 9 letter word STRANGLES
I've seen this crossword clue in The Guardian
S
T
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A
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Buddy explains!

The straight part
We know that "Kills" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case kills = strangles.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 STRANGLES mean?
STRANGLES noun- A disease of horses caused by an infection by the bacterium Streptococcus equi.
- A trading strategy using options, constructed through taking equal positions in a put and a call with different strike prices, such that there is a payoff if the underlying asset's value moves beyond the range of the two strike prices.
- To kill someone by squeezing the throat so as to cut off the oxygen supply; to choke, suffocate or throttle.
- To stifle or suppress.
- To be killed by strangulation, or become strangled.
- To be stifled, choked, or suffocated in any manner.