Man abroad grabbing at politician (7)

I believe the answer is:

senator

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'politician' is the definition.
(I know that senator is a type of legislator)

'man abroad grabbing at' is the wordplay.
'man abroad' becomes 'senor' (Senor is an example. I am not sure about the 'abroad' bit.).
'grabbing' indicates putting letters inside.
'senor' enclosing 'at' is 'SENATOR'.

Can you help me to learn more?

(Other definitions for senator that I've seen before include "Treason committed by member of Upper House" , "Roman politician" , "US politician" , "Member of government" , "Member of upper US assembly" .)

I've seen this clue in The Telegraph and The Sun.

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