Place is buzzing: politician’s beginning significant dodgy argument (7,8)
I believe the answer is:
special pleading
'dodgy argument' is the definition.
(dishonest form of argument)
'place is buzzing politician's beginning significant' is the wordplay.
'buzzing' indicates anagramming the letters (letters buzz around).
'beginning' suggests taking the first letters.
'significant' becomes 'leading' (leading can mean significant or important).
The first letter of 'politicians' is 'p'.
'place'+'is'='placeis'
'placeis' anagrammed gives 'special'.
'special'+'p'+'leading'='SPECIAL PLEADING'
(Another definition for special pleading that I've seen is " One-sided argument".)