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Nearby
supply
cut
by
carpenter,
say,
European
and
Asian
wood
(6,4)
Nearby supply cut by carpenter, say, European and Asian wood (6,4)
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The definition is at the end of the clue.
How the clue works
The Asian wood is built from an anagram of "nearby" (with "supply" working as the anagram indicator, read as supple-ly), giving the letters BANYRE. Then ANT (a carpenter ant, hence "carpenter, say") is inserted — that's the "cut by" containment — splitting it into BANY-ANT-RE. Finally E for European is tacked on the end to make BANYAN TREE.