The most common and most likely answer to this crossword clue is the 5 letter word PESTO
I've seen this crossword clue in The Times
P
E
S
T
O
More clues leading to the result PESTO
- Troublesome insect perhaps over sauce
- Ingredient of recipe, stonking Ligurian food
- Sauce: favourite covering small duck
- Runs out of fast-going sauce
- Bother over sauce
- It’s mainly Basil and Oscar chasing a nuisance
- Ring after annoying person gives one sauce
- Taken from recipes, tomato sauce
- Annoyance with old Italian sauce
- I annoy constantly with bit of obscene sauce
Buddy explains!

The straight part
We know that "sauce" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case sauce = pesto.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 PESTO mean?
PESTO noun- A sauce, especially for pasta, originating from the Genoa region in Italy, made from basil, garlic, pine nuts, olive oil and cheese (usually pecorino)