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' means one lot of letters goes inside another.
'new' is an anagram indicator.
'tree' with letters rearranged gives 'tere'.
'end' going around '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" .)