Favourite you finally pierce, showing bad temper (9)
I believe the answer is:
petulance
'bad temper' is the definition.
(I've seen this before)
'favourite you finally pierce' is the wordplay.
'favourite' becomes 'pet' (synonyms).
'finally' says to take the final letters.
'pierce' becomes 'lance' (lancing is a kind of piercing).
The last letter of 'you' is 'u'.
'pet'+'u'+'lance'='PETULANCE'
'showing' acts as a link.
(Other definitions for petulance that I've seen before include "Bad temper, sulkiness" , "Peevishness" , "Childish sulkiness" , "Sulky bad behaviour" , "Show of temper" .)