Near to top cabinet (6)

I believe the answer is:

closet

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'cabinet' is the definition.
(I've seen this before)

'near to top' is the wordplay.
'near' becomes 'close' (synonyms).
'to top' becomes 't' (I can't justify this - if you can you should believe this answer much more).
'close'+'t'='CLOSET'

Can you help me to learn more?

(Other definitions for closet that I've seen before include "Shut away in private conference - in small room?" , "Secret - cupboard" , "Small cupboard or recess" , "A small room - best to come out of it" , "Furtive" .)

I've seen this clue in the Sydney Morning Herald.

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