Crossword Genius

Arrogant politician breaking river promises to free current (7)

Ross

I believe the answer is:

pompous

I'm a little stuck... Click here to teach me more about this clue!

'arrogant' is the definition.
(I've seen this before)

'politician breaking river promises to free current' is the wordplay.
I cannot really see how this works, but
'politician' could be 'mp' (Member of Parliament) and 'mp' is found in the answer.
'river' could be 'po' (Italian river) and 'po' is found in the answer.
The remaining letters 'ous' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for pompous that I've seen before include "Affectedly self-important" , "Grandly self-important" , "Proud" , "Grandiose" , "Bombastic" .)

I've seen this clue in The Guardian.
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