The boy gets saucy after a half-hour break! (6)
I believe the answer is:
rupert
'the boy' is the definition.
(I've seen this before)
'saucy after a half-hour break' is the wordplay.
'saucy' becomes 'pert' ('pert' can be a synonym of 'saucy'**).
'after' is a charade indicator (letters next to each other).
'a half' means to take half the letters.
'break' is an anagram indicator.
'hour' with half the letters taken is 'ur'.
'ur' anagrammed gives 'ru'.
'pert' after 'ru' is 'RUPERT'.
'gets' is the link.
(Other definitions for rupert that I've seen before include "Boy" , "chap" , "Mary Tourtel's bear" , "Prince" , "Comic strip bear" .)