I blame problems on this Australian senator (6)

I believe the answer is:

lambie

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'australian senator' is the definition.
I know nothing about this answer so I cannot judge whether this works.

'i blame problems on' is the wordplay.
'problems' indicates an anagram (I've seen 'problem' mean this).
'on' indicates putting letters inside (as in clothing 'on' a person).
'blame' with letters rearranged gives 'lambe'.
'i' going within 'lambe' is 'LAMBIE'.

'this' acts as a link.

Can you help me to learn more?

(Another definition for lambie that I've seen is " Cosset".)

I've seen this clue in the Sydney Morning Herald.

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