Starter taken off mat that's greasy (4)
I believe the answer is:
oily
'that's greasy' is the definition.
(synonyms)
I cannot understand how the rest of the clue works.
Can you help me to learn more?
(Other definitions for oily that I've seen before include "Like a lot of fish" , "Oleaginous" , "Unctuous" , "Smarmy" , "Viscous" .)