Crossword Genius

Governing bodies in London region given additional seat (7)

Ross

I believe the answer is:

senates

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'governing bodies' is the definition.
(I've seen this in another clue)

'london region given additional seat' is the wordplay.
'london region' becomes 'SE' (South East postcode).
'given additional seat' becomes 'nates' (I can't explain this - if you can you should give a lot more credence to this answer).
'se'+'nates'='SENATES'

'in' is the link.

Can you help me to learn more?

(Other definitions for senates that I've seen before include "Political bodies" , "Governing bodies" .)

I've seen this clue in The Times.
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