Eat up Lucy's chewing gum (10)
I believe the answer is:
eucalyptus
'gum' is the definition.
(I know that eucalyptus is a type of gum)
'eat up lucy's chewing' is the wordplay.
'chewing' indicates anagramming the letters.
'eat'+'up'+'lucys'='eatuplucys'
'eatuplucys' anagrammed gives 'EUCALYPTUS'.
(Other definitions for eucalyptus that I've seen before include "Australasian tree" , "Evergreen tree" , "Australian tree yielding gum and oil" .)