Tree full of bats, potentially? (6)

I believe the answer is:

willow

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'tree' is the definition.
(willow tree is a kind of tree)

I don't understand the remainder of the clue.

(Other definitions for willow that I've seen before include "One [TYPE OF TREE]" , "Common riverside tree" , "Osier; cricket bat" , "Pussy- - -" , "Fast-growing tree" .)

I've seen this clue in the Evening Standard.

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