Good chap's sound for Prime Minister (9)
I believe the answer is:
gladstone
'prime minister' is the definition.
(William Ewart Gladstone Prime Minister 1868-1894)
'good chap's sound' is the wordplay.
'good' becomes 'g' (abbreviation).
'chap's' becomes 'lads'.
'sound' becomes 'tone' (tone is a kind of sound**).
'g'+'lads'+'tone'='GLADSTONE'
'for' is the link.
(Other definitions for gladstone that I've seen before include "Liberal leader" , "PM no longer" , "Victorian GOM" , "So tangled up with old British Prime Minister" , "Victorian PM" .)