Greek character ringing old boy over a fear (6)
I believe the answer is:
phobia
'fear' is the definition.
(a phobia is a fear of a particular thing)
'greek character ringing old boy over a' is the wordplay.
'greek character' becomes 'phi' (letter from the Greek alphabet).
'ringing' is an insertion indicator.
'old boy' becomes 'OB' (abbreviation for a private school 'old boy').
'over' means one lot of letters go next to another (in a down clue, some letters go over others).
'phi' enclosing 'ob' is 'phobi'.
'phobi'+'a'='PHOBIA'
(Other definitions for phobia that I've seen before include "Irrational fear (of thing)" , "Great fear of something" , "A lasting abnormal fear or dislike" , "Extreme and irrational fear" , "Overpowering fear" .)