Sue put lacy bits up with gum (10)

I believe the answer is:

eucalyptus

I'm a little stuck... Click here to teach me more about this clue!

'gum' is the definition.
(I know that eucalyptus is a type of gum)

'sue put lacy bits up' is the wordplay.
'sue put lacy' anagrams to 'EUCALYPTUS'.
But, I'm not sure how the anagram is indicated.

'with' acts as a link.

Can you help me to learn more?

(Other definitions for eucalyptus that I've seen before include "Evergreen tree" , "Australasian tree" , "Australian tree yielding gum and oil" .)

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

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