Sweeping support for military advisors (7,5)

I believe the answer is:

general staff

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'for military advisors' is the definition.
I can't judge whether this definition defines the answer.

'sweeping support' is the wordplay.
'sweeping' becomes 'general' (I've seen this before).
'support' becomes 'staff' (I can't justify this - if you can you should believe this answer much more).
'general'+'staff'='GENERAL STAFF'

Can you help me to learn more?

(Other definitions for general staff that I've seen before include "Military planners" , "Senior officer's aides" , "Commander's assistants" .)

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

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