Puritanical sort of curmudgeon needing internal examination? (9)
I believe the answer is:
moraliser
'puritanical sort' is the definition.
(a puritanical person)
'curmudgeon needing internal examination?' is the wordplay.
'curmudgeon' becomes 'miser' (both can mean a selfish or bad-tempered person).
'needing internal' means one lot of letters goes inside another.
'examination?' becomes 'oral' (oral is a kind of examination).
'miser' placed around 'oral' is 'MORALISER'.
'of' is the link.
(Other definitions for moraliser that I've seen before include "Ethical speaker" , "preacher" .)