Self-confidence of a doctor behind Middle East organisation (6*)
I believe the answer is:
Here is my best explanation:
'self-confidence' is the definition.
'a doctor behind middle east organisation' is the wordplay.
'doctor' becomes 'mb' (Bachelor of Medicine, Medicinae Baccalaureus).
'behind' means one lot of letters go next to another.
'middle east organisation' becomes 'plo' (I can't explain this - if you can you should believe this answer much more).
'mb' after 'plo' is 'plomb'.
'of' is the link.
(Other definitions for aplomb that I've seen before include "Sangfroid", "Self-possession, assurance", "Self-satisfied dignity and confidence", "Self-satisfied assurance", "Self-confidence, assurance", "Composure", "Great coolness and composure under strain", "Pompous dignity or poise", "Self-assurance" and "Cool self-assurance".)