The most common and most likely answer to this crossword clue is the 5 letter word NAPOO
I've seen this crossword clue in Financial Times
N
A
P
O
O
More clues leading to the result NAPOO
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 = napoo.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 NAPOO mean?
NAPOO verb- To finish; to put an end to; to kill.
- Finished, dead, no more, gone; non-existent.
- Dead.
- There is no more.