Being outside, claim to be working assiduously (9)

I believe the answer is:

beavering

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'working assiduously' is the definition.
'beavering' can be an answer for 'working' (beavering is a kind of working). I am not certain of the 'assiduously' bit.

'being outside claim' is the wordplay.
'outside' means one lot of letters goes inside another.
'claim' becomes 'aver' (I've seen this in another clue).
'being' enclosing 'aver' is 'BEAVERING'.

'to be' acts as a link.

Can you help me to learn more?

(Another definition for beavering that I've seen is " working hard".)

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

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