Politician always backward-looking, noxious air nauseating, ultimately (4-4)
I believe the answer is:
rees-mogg
'politician' is the definition.
(Jacob Rees-Mogg is a British MP)
'always backward-looking noxious air nauseating ultimately' is the wordplay.
'always' becomes 'eer' (poetic way of saying ever).
'backward-looking' shows that the letters should be reversed in order.
'noxious air' becomes 'smog' (smog is fog caused by pollution).
'ultimately' says to take the final letters.
The final letter of 'nauseating' is 'g'.
'eer' back-to-front is 'ree'.
'ree'+'smog'+'g'='REES-MOGG'
(Another definition for rees-mogg that I've seen is " relic".)