Dropped quiet with media bosses around department (7)

I believe the answer is:

shedded

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'media bosses around department' is the definition.
I can't tell whether this definition defines the answer.

'dropped quiet' is the wordplay.
'dropped' becomes 'shed' ('shed' can be a synonym of 'drop').
'quiet' becomes 'ded' (I can't explain this - if you can you should believe this answer much more).
'shed'+'ded'='SHEDDED'

'with' acts as a link.

Can you help me to learn more?

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

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