Brother Kenneth's little bust (6)
I believe the answer is:
broken
'bust' is the definition.
(I've seen this before)
'brother kenneth's little' is the wordplay.
'brother' becomes 'bro' (short for brother).
'kenneth's' becomes 'ken's' (short for Kenneth).
'little' means to remove the last letter (the word is not quite complete).
'kens' with its last letter removed is 'ken'.
'bro'+'ken'='BROKEN'
(Other definitions for broken that I've seen before include "Defective" , "If it's not ..., don't fix it" , "out of order" , "Bust" , "faulty" .)