Distributed tape with uncle showing peevish irritation (9)
I believe the answer is:
petulance
'peevish irritation' is the definition.
(I've seen this before)
'distributed tape with uncle' is the wordplay.
'distributed' is an anagram indicator.
'with' is a charade indicator (letters next to each other).
'tape'+'uncle'='tapeuncle'
'tapeuncle' is an anagram of 'PETULANCE'.
'showing' is the link.
(Other definitions for petulance that I've seen before include "Childish sulkiness" , "Bad temper, sulkiness" , "Show of temper" , "Peevish irritation" , "ill humour" .)