Government department, one fashionable in the sixties (3)

I believe the answer is:

mod

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'government department' is the definition.
(Ministry of Defence)

I don't understand how the remainder of the clue works.

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(Other definitions for mod that I've seen before include "Meeting of the Scottish" , "Gaelic literary festival" , "ministry" , "Rocker's rival?" , "1960s teenager" .)

I've seen this clue in The Times.

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