Greek poet loses right to residence (4)
I believe the answer is:
home
'to residence' is the definition.
(home is a kind of residence)
'greek poet loses right' is the wordplay.
'greek poet' becomes 'Homer' (ancient Greek poet).
'loses' indicates named letters should be taken away.
'right' becomes 'r' (common abbreviation).
'homer' with 'r' taken out is 'HOME'.
(Other definitions for home that I've seen before include "dwelling house" , "Be it ever so humble, there's no place like it" , "Living place" , "It's where the heart is, they say" , "birthplace" .)