Villain appears day after day in tree (5)
I believe the answer is:
baddy
'villain' is the definition.
(bad guy in a story)
'day after day in tree' is the wordplay.
'day after day' becomes 'DD' (two abbreviations for day).
'in' indicates putting letters inside.
'tree' becomes 'bay' (bay is a kind of tree).
'dd' going into 'bay' is 'BADDY'.
'appears' acts as a link.
(Other definitions for baddy that I've seen before include "illain" , "Villain in book or film" .)