The most common and most likely answer to this crossword clue is the 9 letter word ITCHINESS
I've seen this crossword clue in The Times
I
T
C
H
I
N
E
S
S
More clues leading to the result ITCHINESS
- Feeling of irritation in chest is awful
- Impatience in chess? It’s disastrous
- Wound in chest is something irritating
- Irritation born out of spite
- Unpleasant sensation is in chest possibly
- It's kept around some Asians briefly to produce an irritating sensation
- Sensational experience where island girl drinks punch
- Blundering in chess? It’s an irritating feeling!
Buddy explains!

The straight part
We know that "something irritating" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case something irritating = itchiness.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.