Old boy, Greek character, entering a slum for demolition (7)
I believe the answer is:
alumnus
'old boy' is the definition.
(I've seen this before)
'greek character entering a slum for demolition' is the wordplay.
'greek character' becomes 'nu' (letter from the Greek alphabet).
'entering' means one lot of letters goes inside another.
'for demolition' indicates an anagram (I've seen this in other clues).
'a'+'slum'='aslum'
'aslum' is an anagram of 'alums'.
'nu' placed into 'alums' is 'ALUMNUS'.
(Other definitions for alumnus that I've seen before include "Old pupil" , "Ex-pupil" , "Former school pupil" , "School or college graduate" , "Former pupil or student" .)