'More just do right', the compiler admitted (6)
I believe the answer is:
fairer
'more just' is the definition.
('fair' can be a synonym of 'just')
'do right the compiler admitted' is the wordplay.
'do' becomes 'fare' ('fare' can be a synonym of 'do'**).
'right' becomes 'r' (common abbreviation).
'the compiler' becomes 'i' (the person who is writing these clues).
'admitted' means one lot of letters goes inside another.
'fare'+'r'='farer'
'farer' placed around 'i' is 'FAIRER'.
(Other definitions for fairer that I've seen before include "Less inclined to show bias" , "More equitable or blonde" , "Cleaner" , "lighter" , "More blond or equitable" .)