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' ('end' can be a synonym of 'finish'**).
'with' means one lot of letters goes inside another.
'new' indicates anagramming the letters.
'tree' with letters rearranged gives 'tere'.
'end' enclosing 'tere' is 'ENTERED'.
'to' acts as a 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" .)