Pruning citrus then opening bank branch (4)

I believe the answer is:

limb

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'branch' is the definition.
(I know that limb is a type of branch)

'pruning citrus then opening bank' is the wordplay.
'pruning citrus then' becomes 'lim' (I can't justify this - if you can you should give a lot more credence to this answer).
'opening' indicates taking the first letters.
The initial letter of 'bank' is 'b'.
'lim'+'b'='LIMB'

Can you help me to learn more?

(Other definitions for limb that I've seen before include "Arm, leg or wing" , "Human's extension" , "Jointed appendage" , "Eg, arm, leg" , "A supporter" .)

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

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