The most common and most likely answer to this crossword clue is the 7 letter word GALLING
G
A
L
L
I
N
G
More clues leading to the result GALLING
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 = galling.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 GALLING mean?
GALLING verb- To bother or trouble.
- To harass, to harry, often with the intent to cause injury.
- To chafe, to rub or subject to friction; to create a sore on the skin.
- To exasperate.
- To cause pitting on a surface being cut from the friction between the two surfaces exceeding the bond of the material at a point.
- To scoff; to jeer.
- To impregnate with a decoction of gallnuts in dyeing.
- Wear caused by adhesion between sliding surfaces.
- Vexing, humiliating