Silly bet -- let in a chap to be the deciding factor (3,3,7)
I believe the answer is:
tip the balance
'be the deciding factor' is the definition.
(I've seen this before)
'silly bet let in a chap' is the wordplay.
'silly' is an anagram indicator.
'bet'+'let'+'in'+'a'+'chap'='betletinachap'
'betletinachap' with letters rearranged gives 'TIP THE BALANCE'.
'to' acts as a link.
(Other definitions for tip the balance that I've seen before include "Make small, decisive, difference" , "Be the deciding factor" .)