The most common and most likely answer to this crossword clue is the 8 letter word RANKLING
I've seen this crossword clue in The Times
R
A
N
K
L
I
N
G
More clues leading to the result RANKLING
Buddy explains!

The straight part
We know that "causing annoyance" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case causing annoyance = rankling.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 RANKLING mean?
RANKLING verb- To cause irritation or deep bitterness.
- To fester.
- A sensation that rankles.