British security resembling Big Brother? On the contrary (3)

I believe the answer is:

sis

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'brother? on the contrary' is the definition.
'sis' can be an answer for 'brother?' (thesaurus). I am unsure of the 'on the contrary' bit.

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

Can you help me to learn more?

(Other definitions for sis that I've seen before include "Relative's" , "Sibling (informal)" , "Secret Intelligence Service (abbreviation)" , "relative" , "Girl" .)

I've seen this clue in The Independent.

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