One entering test after old king in lesson (8)
I believe the answer is:
tutorial
'lesson' is the definition.
(I've seen this before)
'one entering test after old king' is the wordplay.
'one' becomes 'i' (Roman numeral).
'entering' indicates putting letters inside.
'test' becomes 'oral' (oral is a type of examination).
'after' says to put letters next to each other.
'old king' becomes 'tut' (King Tut).
'i' put into 'oral' is 'orial'.
'orial' after 'tut' is 'TUTORIAL'.
'in' is the link.
(Other definitions for tutorial that I've seen before include "University study period" , "Session of intensive teaching to an individual or small group" , "Period of teaching as from college lecturer" , "University lesson" , "Seminar" .)