Extremely sociably, doctor, a young Greek girl and sibling form a partnership (9)
I believe the answer is:
symbiosis
'partnership' is the definition.
(I've seen this before)
'extremely sociably doctor a young greek girl and sibling' is the wordplay.
'extremely' suggests removing the centre (only the extremes of the word are used).
'doctor' becomes 'MB' (Bachelor of Medicine, Medicinae Baccalaureus).
'a young greek girl' becomes 'io' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'and' is a charade indicator (letters next to each other).
'sibling' becomes 'sis' (short for sister).
'sociably' with its centre taken out is 'sy'.
'sy'+'mb'+'io'+'sis'='SYMBIOSIS'
'form a' acts as a link.
This may not be correct. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for symbiosis that I've seen before include "Dissimilar organisms living together for mutual advantage" , "Mutual interaction between different organisms" , "Advantageous interaction between different organisms" , "Co-dependent existence" , "close relationship" .)