Pamper group on Greek island (6)
I believe the answer is:
cosset
'pamper' is the definition.
('cosset' can be a synonym of 'pamper')
'group on greek island' is the wordplay.
'group' becomes 'set' (set is a kind of group).
'on' is a charade indicator (letters next to each other).
'greek island' becomes 'cos' (I've seen this before).
'set' put after 'cos' is 'COSSET'.
(Other definitions for cosset that I've seen before include "Pamper, coddle (6)" , "Nanny" , "Protect overindulgently" , "Care for and protect" , "Overindulge" .)