Intend shortly to enclose grey brain part (7)
I believe the answer is:
medulla
'brain part' is the definition.
('medulla' is part of 'brain')
'intend shortly to enclose grey' is the wordplay.
'intend' becomes 'mean' (meaning is a kind of intending).
'shortly' means to remove the last letter.
'to enclose' is an insertion indicator.
'grey' becomes 'dull' (I can't explain this - if you can you should believe this answer much more).
'mean' with its final letter removed is 'mea'.
'mea' going around 'dull' is 'MEDULLA'.
Can you help me to learn more?
(Other definitions for medulla that I've seen before include "Innards of organ" , "Lower part of the brain" , "bit of brain" , "pith" , "centre of organ" .)