Protection from sunlight certainly possessed in centre of Greece (8)
I believe the answer is:
eyeshade
'protection from sunlight' is the definition.
(an eyeshade protects your eyes from the sun)
'certainly possessed in centre of greece' is the wordplay.
'certainly' becomes 'yes' (both can be used to answer in the affirmative).
'possessed' becomes 'had' (to have something is to possess it).
'in' indicates putting letters inside.
'centre of' means to look at the middle letters.
The middle of 'greece' is 'ee'.
'yes'+'had'='yeshad'
'yeshad' inserted into 'ee' is 'EYESHADE'.
(Other definitions for eyeshade that I've seen before include "something like CAP" , "Protective visor" , "guard" , "Visor to protect from strong light" , "Translucent visor" .)