Hunt with zeal shaking fruit from tree (8)

I believe the answer is:

hazelnut

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'fruit from tree' is the definition.
'hazelnut' can be an answer for 'tree' (hazelnut tree is a kind of tree). I'm not sure about the 'fruit from' bit.

'hunt with zeal shaking' is the wordplay.
'with' means one lot of letters go next to another.
'shaking' is an anagram indicator.
'hunt' after 'zeal' is 'zealhunt'.
'zealhunt' is an anagram of 'HAZELNUT'.

Can you help me to learn more?

(Other definitions for hazelnut that I've seen before include "Filbert or cob" , "Cobnut or filbert" .)

I've seen this clue in The Sun.

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