Instructed old king and old socialist (7)
I believe the answer is:
tutored
'instructed' is the definition.
(tutoring is a kind of instructing)
'old king and old socialist' is the wordplay.
'old king' becomes 'tut' (King Tut).
'and' is a charade indicator (letters next to each other).
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'socialist' becomes 'red' (red is a kind of socialist).
'tut'+'o'+'red'='TUTORED'
(Other definitions for tutored that I've seen before include "Coached" , "Privately taught" , "Trained" , "Rude tot (anag.)" , "Taught small groups" .)