The most common and most likely answer to this crossword clue is the 10 letter word ANNIHILATE
I've seen this crossword clue in Independent
A
N
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More clues leading to the result ANNIHILATE
- Take out girl — one I left consumed with passion
- Whitewash a thin line with a compound
- Ensure no more is heard of girl I abhor, hugging the Italian?
- Wipe out Athenian rebels, saving the Italian
- Hit an alien, given new order to destroy
- Rub out a thin line scrawled around answer
- Hammer a nail in the bust
- Prepare Italian hen for slaughter
- Hit an alien deployed to massacre
Buddy explains!

The straight part
We know that "Ensure no more is heard of" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case ensure no more is heard of = annihilate.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 ANNIHILATE mean?
ANNIHILATE verb- To reduce to nothing, to destroy, to eradicate.
- To react with antimatter, producing gamma radiation.
- To treat as worthless, to vilify.
- To render null and void; to abrogate.