A workroom in the house for a department of state (4,6)

I believe the answer is:

home office

I believe this clue is a double definition.

'a workroom in the house' is the first definition.
(office in one's home)

'a department of state' is the second definition.
(government department)

'for' acts as a link.

(Another definition for home office that I've seen is " Government department".)

I've seen this clue in The Times.

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