Oil from Greek facility (6)
I believe the answer is:
grease
'oil' is the definition.
(grease is a kind of oil)
'greek facility' is the wordplay.
'greek' becomes 'gr'.
'facility' becomes 'ease' (I've seen this before).
'gr'+'ease'='GREASE'
'from' is the link.
(Other definitions for grease that I've seen before include "-- gun; -- monkey" , "Musical starring John Travolta and Olivia Newton-John" , "Musical animal fat?" , "Possible cause of slip-up" , "Fully aware, astonished" .)