The most common and most likely answer to this crossword clue is the 4 letter word PEST
I've seen this crossword clue in Independent
P
E
S
T
More clues leading to the result PEST
- Half of capital being lost is a nuisance
- Plump louse eats plant ends, causing blight
- Nuisance if clergyman loses grail regularly
- Old Bob in sulk becoming a nuisance
- Bother minister eschewing religious studies
- Paddy harbours small annoyance
- Endless sauce, an annoyance
- Capital half lost — that’s a nuisance
- Exercise on street to get troublemaker
- 20 apes tried clothes
Buddy explains!

The straight part
We know that "Nuisance" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case nuisance = pest.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 PEST mean?
PEST noun- A plague, pestilence, epidemic
- Any destructive insect or caterpillar that attacks crops or livestock; an agricultural pest.
- An annoying person, a nuisance.
- An animal regarded as a nuisance, destructive, or a parasite, vermin.
- An invasive weed.