The most common and most likely answer to this crossword clue is the 8 letter word IRRITATE
I've seen this crossword clue in The Daily Telegraph
I
R
R
I
T
A
T
E
More clues leading to the result IRRITATE
- Anger and fury about dreadful trait
- Vex one briefly slowing in speed
- Bother to supply water — that takes time where there’s gallons
- Put out and angry about instruction to reduce speed
- Mad keeping close to commuter, it gives you bug
- Make annoyed and angry about unfinished ceremony
- Provoke and mock bishop coming in for mass
- Needle slowing jabs up in arms
- Scientists taking time to bisect livid bug
- Annoy Irish coming over in improper attire
Buddy explains!

The straight part
We know that "Annoy" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case annoy = irritate.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 IRRITATE mean?
IRRITATE verb- To provoke impatience, anger, or displeasure in.
- To cause or induce displeasure or irritation.
- To induce pain in (all or part of a body or organism).
- To render null and void.