One politician to act with cogency (6)

I believe the answer is:

impact

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'cogency' is the definition.
Although both the answer and definition are singular nouns, I don't understand how they can define each other.

'one politician to act' is the wordplay.
'one' becomes 'i' (Roman numeral).
'politician' becomes 'MP' (Member of Parliament).
'i'+'mp'+'act'='IMPACT'

'with' is the link.

Can you help me to learn more?

(Other definitions for impact that I've seen before include "Repercussion" , "Result" , "Forcible contact between two things" , "The force of one body against another" , "Forceful contact between two objects" .)

I've seen this clue in the Evening Standard.

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