Shake tree, perhaps, where there's cuckoo I feed a lot (9)

I believe the answer is:

defoliate

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'shake tree perhaps where' is the definition.
I can't tell whether this definition defines the answer.

'cuckoo i feed a lot' is the wordplay.
'cuckoo' indicates an anagram (I've seen this in other clues).
'i'+'feed'+'a'+'lot'='ifeedalot'
'ifeedalot' with letters rearranged gives 'DEFOLIATE'.

'there's' acts as a link.

Can you help me to learn more?

(Another definition for defoliate that I've seen is " Remove leaves".)

I've seen this clue in The Guardian.

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