The most common and most likely answer to this crossword clue is the 5 letter word RATTY
I've seen this crossword clue in The Times
R
A
T
T
Y
More clues leading to the result RATTY
- Irritable man admits drinking nothing alcoholic
- Irritable and childishly ill-behaved, destroying book
- Irritable, getting dry in a little sun
- Easily annoyed a couple of times aboard railway
- Ill-behaved but beginning to be irritable
- Hint: about 12 short
- Bad-tempered fellow seizes sporting trophy
- Short races some hope to hold?
- Bad-tempered blackleg, extremely testy
- Bad-tempered note about not drinking
Buddy explains!

The straight part
We know that "Easily annoyed" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case easily annoyed = ratty.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 RATTY mean?
RATTY adjective- Similar to a rat; ratlike.
- Infested with rats.
- In poor condition or repair
- Irritable, annoyed, bad-tempered.