Came in to finish with new tree (7)
I believe the answer is:
entered
'came in' is the definition.
('enter' can be a synonym of 'come in')
'finish with new tree' is the wordplay.
'finish' becomes 'end' (come to an end).
'with' indicates putting letters inside.
'new' indicates an anagram.
'tree' is an anagram of 'tere'.
'end' enclosing 'tere' is 'ENTERED'.
'to' is the link.
(Other definitions for entered that I've seen before include "Put down" , "Went in and registered as competitor" , "moved in" , "Logged; arrived" , "Enrolled or went in" .)