The most common and most likely answer to this crossword clue is the 7 letter word TSETSES
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More clues leading to the result TSETSES
Buddy explains!

The straight part
We know that "Nasty nippers" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case nasty nippers = tsetses.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 TSETSES mean?
TSETSES noun- Any fly of the genus Glossina, native to Africa, that feeds on human and animal blood; known primarily as a carrier of parasitic trypanosomes.