Greek poet lacks right of residence (4)
I believe the answer is:
home
'residence' is the definition.
(I know that residence can be written as home)
'greek poet lacks right' is the wordplay.
'greek poet' becomes 'Homer' (ancient Greek poet).
'lacks' is a deletion indicator.
'right' becomes 'r' (common abbreviation).
'homer' with 'r' removed is 'HOME'.
'of' acts as a link.
(Other definitions for home that I've seen before include "Domicile" , "Place of origin" , "chez nous?" , "Residence" , "goal" .)