Head of state's mature wise man (4)
I believe the answer is:
sage
'wise man' is the definition.
(sage is a kind of wise man)
'head of state's mature' is the wordplay.
'head of' says to take the initial letters.
'mature' becomes 'age' ('age' can be a synonym of 'mature'**).
The first letter of 'state' is 's'.
's'+'age'='SAGE'
(Other definitions for sage that I've seen before include "Profoundly wise" , "Wise man - flavoursome plant" , "Man of wisdom" , "Wise woman" , "Fragrant herb having wisdom" .)