A matter-of-fact doctrine is dividing the kingdom (7)
I believe the answer is:
realism
'a matter-of-fact doctrine' is the definition.
'realism' can be an answer for 'doctrine' (realism is a kind of doctrine). I am not sure about the 'a matter-of-fact' bit.
'is dividing the kingdom' is the wordplay.
'dividing' means one lot of letters goes inside another (inserted letters divide the word).
'the kingdom' becomes 'realm' (kingdom is a type of country or realm).
'is' inserted into 'realm' is 'REALISM'.
Can you help me to learn more?
(Other definitions for realism that I've seen before include "True to life quality" , "Art genre that is true to life" , "Artistic movement representing people and things as they actually are" , "Seeing things as they are" , "Representation in an accurate and true to life way" .)