The most common and most likely answer to this crossword clue is the 6 letter word SHIRTY
I've seen this crossword clue in The Daily Telegraph
S
H
I
R
T
Y
Buddy explains!

The straight part
We know that "Ill-tempered" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case ill-tempered = shirty.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 SHIRTY mean?
SHIRTY adjective- Ill-tempered or annoyed.