Covered in grease like cooked eggs, surface wiped (5)
I believe the answer is:
oiled
'covered in grease' is the definition.
'cooked eggs surface wiped' is the wordplay.
'cooked eggs' becomes 'boiled'.
'surface wiped' means to remove the first letter.
'boiled' with its initial letter taken off is 'OILED'.
'like' is the link.
(Other definitions for oiled that I've seen before include "Anointed" , "Oldie (anag)" , "running smoothly?" , "Lubricated or drunk" , "Lubricated (with drink?)" .)