Country producing oil we hear (6)
I believe the answer is:
Here is my best explanation:
'country' is the definition.
(Greece is an example)
'oil we hear' is the wordplay.
'oil' becomes 'grease' (grease is a kind of oil).
'we hear' shows a homophone (sound like).
'grease' is a homophone of 'GREECE'.
'producing' is the link.
(Other definitions for greece that I've seen before include "in E", "Mediterranean republic", "Hellenic Republic", "Southern European country", "Athens its capital", "Country of southeast Europe", "Country of southern Europe", "Hellenic republic", "Nation" and "European state".)