Variety of native tree that's deep-rooted (10)
I believe the answer is:
inveterate
'deep-rooted' is the definition.
(thesaurus)
'variety of native tree' is the wordplay.
'variety of' indicates anagramming the letters.
'native'+'tree'='nativetree'
'nativetree' with letters rearranged gives 'INVETERATE'.
'that's' acts as a link.
(Other definitions for inveterate that I've seen before include "Confirmed in (bad) habit" , "long-standing" , "Hardened" , "Long-established" , "Long-formed (bad habit)" .)