The most common and most likely answer to this crossword clue is the 7 letter word ANNOYED
I've seen this crossword clue in The Daily Telegraph
A
N
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O
Y
E
D
More clues leading to the result ANNOYED
- Cross ground one day, bearing north
- Fantastic day, none getting fed up
- What’s surprisingly anodyne makes one cross
- Queen admitting heartless obstinacy, dead upset
- Cross girl you had once found harbouring love
- Princess Royal holds in yell. Daughter gets riled
- PA system initially failing, Milliband is peeved
- Crotchety when anyone goes off key
- An irritated doyen describing his state of mind
- Cross one day out around mid-evening
Buddy explains!

The straight part
We know that "peeved" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case peeved = annoyed.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 ANNOYED mean?
ANNOYED verb- To disturb or irritate, especially by continued or repeated acts; to bother with unpleasant deeds.
- To do something to upset or anger someone; to be troublesome.
- To molest; to harm; to injure.
- Troubled, irritated by something unwanted or unliked (an annoyance); vexed.