Pseudo intellectual's beginning to reform incestuous king (7)
I believe the answer is:
oedipus
'incestuous king' is the definition.
(figure of Greek myth)
'pseudo intellectual's beginning to reform' is the wordplay.
'beginning to' indicates taking the first letters.
'reform' indicates an anagram.
The initial letter of 'intellectual' is 'i'.
'pseudo'+'i'='pseudoi'
'pseudoi' is an anagram of 'OEDIPUS'.
(Other definitions for oedipus that I've seen before include "Tragic Greek king in Opus Dei" , "Mythological king who killed his father and married his mother" , "King known for complex" , "He solved Sphinx's riddle" , "Theban who married his mother" .)