Boy king, one talking tediously about one's schooling (7)
I believe the answer is:
tuition
'schooling' is the definition.
(both can mean teaching)
'boy king one talking tediously about one's' is the wordplay.
'boy king' becomes 'Tut' (Tutankhamun).
'one talking tediously' becomes 'ion' (I can't justify this - if you can you should believe this answer much more).
'about' means one lot of letters goes inside another.
'one' becomes 'i' (Roman numeral).
'tut'+'ion'='tution'
'tution' enclosing 'i' is 'TUITION'.
Can you help me to learn more?
(Other definitions for tuition that I've seen before include "Teaching, instruction" , "Training" , "Teaching, often one-to-one" , "Personal coaching" , "practice" .)