Specialist sending back anything that's not thin and green (13)
I believe the answer is:
gynaecologist
'specialist' is the definition.
(gynaecologist is a kind of specialist)
'not thin and green' is the wordplay.
'not thin' becomes 'gyna' (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).
'green' becomes 'ecologist'.
'gyna'+'ecologist'='GYNAECOLOGIST'
'sending back anything that's' is the link.
This may not be right. Some or all of it may belong to another bit of the clue.
(Other definitions for gynaecologist that I've seen before include "Specialist in women's reproductive organs" , "Expert in female diseases" , "Doctor for women" , "Specialist in diseases of women" .)