The most common and most likely answer to this crossword clue is the 9 letter word IRRITABLE
I
R
R
I
T
A
B
L
E
More clues leading to the result IRRITABLE
- Irish woman starts to become loud and extremely easily annoyed
- One bishop, one on board, is cranky
- Blairite prepared to accept leader of Red Cross
- Bishop among pair in Rome by altar, say, and cross
- Impatient bishop entering couple on register
- Short-tempered Blairite worried about right
- Easily annoyed, showing a lot of anger, anger about bill
- Cross a road, first reaching a bar
- Easily annoyed, bishop being pressed by two internationals on board
Buddy explains!

The straight part
We know that "Cross" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case cross = irritable.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 IRRITABLE mean?
IRRITABLE adjective- Capable of being irritated.
- Easily exasperated or excited.
- Responsive to stimuli.