Favourite uncle somehow hiding a bad temper (9)
I believe the answer is:
petulance
'bad temper' is the definition.
(I've seen this before)
'favourite uncle somehow hiding a' is the wordplay.
'favourite' becomes 'pet' ('pet' can be a synonym of 'favourite').
'somehow' indicates anagramming the letters.
'hiding' indicates putting letters inside.
'uncle' with letters rearranged gives 'ulnce'.
'ulnce' enclosing 'a' is 'ulance'.
'pet'+'ulance'='PETULANCE'
(Other definitions for petulance that I've seen before include "ill humour" , "Show of temper" , "Peevish irritation" , "Childish sulkiness" , "Sulky bad behaviour" .)