Primes secretary to go, turning up at home (4)

I believe the answer is:

semi

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But I can't explain it at all! Could you help me understand?

(Other definitions for semi that I've seen before include "House sharing a wall" , "eg Half a house" , "half would do!" , "Type of house (UK) - type of truck (US)" , "Property attached to another" .)

I've seen this clue in The Mirror.

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