Favourite clue solved about article in bad temper (9)
I believe the answer is:
petulance
'bad temper' is the definition.
(I've seen this before)
'favourite clue solved about article' is the wordplay.
'favourite' becomes 'pet' (synonyms).
'solved' is an anagram indicator (the anagram must be solved).
'about' is an insertion indicator.
'article' becomes 'an' (English indefinite article).
'clue' anagrammed gives 'ulce'.
'ulce' placed around 'an' is 'ulance'.
'pet'+'ulance'='PETULANCE'
'in' acts as a link.
(Other definitions for petulance that I've seen before include "Bad temper, sulkiness" , "Childish sulkiness" , "ill humour" , "Sulky bad behaviour" , "Peevish irritation" .)