... when tipped about minister promoting riddance of toxic waste (9)

I believe the answer is:

eliminant

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

'riddance of toxic waste' is the definition.
The definition suggests a singular noun which matches the answer.

'when tipped about minister promoting' is the wordplay.
I cannot quite understand how this works, but
'about' could be 'a' (abbreviation in Chambers) and 'a' is found within the answer.
'minister' could be 'min' (abbreviation) and 'min' is present in the answer.
This explanation may well be incorrect...

Can you help me to learn more?

(Another definition for eliminant that I've seen is " A canceling agent; main inlet (anag.)".)

I've seen this clue in The Independent.

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