Crossword Genius

A cornet, or parts of one (4)

Ross

I believe the answer is:

cone

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'a cornet' is the definition.
(thesaurus)

'parts of one' is the wordplay.
'parts of' becomes 'c' (I can't justify this - if you can you should give a lot more credence to this answer).
'c'+'one'='CONE'

'or' acts as a link.

Can you help me to learn more?

(Other definitions for cone that I've seen before include "may obstruct lane" , "Tapering object" , "99, maybe" , "Element of geometry" , "Geometrical figure (used on roads!)" .)

I've seen this clue in the Evening Standard.
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