Madness of king's advancing years (4)
I believe the answer is:
rage
'madness' is the definition.
('rage' can be a synonym of 'madness')
'king's advancing years' is the wordplay.
'king' becomes 'r' (r is abbreviation for rex).
'advancing years' becomes 'age' ('age' can be a synonym of 'years'. I am not sure about the 'advancing' bit.**).
'r'+'age'='RAGE'
'of' is the link.
Can you help me to learn more?
(Other definitions for rage that I've seen before include "Temper - fashion" , "storm" , "Gear up in violent temper" , "Speak with great anger" , "Violent anger, maybe on road" .)