Female minister's in top role (12)

I believe the answer is:

directorship

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'top role' is the definition.
The definition and answer can be both acts as well as being singular nouns.
Maybe you can see a link between them that I can't see?

'female minister's in' is the wordplay.
'female' becomes 'di' (I can't explain this - if you can you should give a lot more credence to this answer).
'minister's' becomes 'rectors' ('rector' can be a synonym of 'minister').
'in' becomes 'hip' (both can mean fashionable).
'di'+'rectors'+'hip'='DIRECTORSHIP'

Can you help me to learn more?

(Another definition for directorship that I've seen is " special position on board".)

I've seen this clue in The Telegraph.

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