Politician, smart, meets gammon? (7)

I believe the answer is:

burnham

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'politician' is the definition.
I don't know anything about this answer so I cannot judge whether this works.

'smart meets gammon?' is the wordplay.
I cannot quite see how this works, but
'smart' could be 'burn' (burning is a kind of smarting) and 'burn' is located in the answer.
'gammon?' could be 'ham' ('ham' can be a synonym of 'gammon') and 'ham' is found within the answer.
No letters remain.
This explanation may well be incorrect...

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I've seen this clue in The Independent.

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