Dirty son with something greasy (4)
I believe the answer is:
soil
'dirty' is the definition.
(I know that dirty can be written as soil)
'son with something greasy' is the wordplay.
'son' becomes 's' (genealogical abbreviation for son).
'with' means one lot of letters go next to another.
'something greasy' becomes 'oil' (oil is greasy).
's'+'oil'='SOIL'
(Other definitions for soil that I've seen before include "Earth; make dirty" , "In which plants grow" , "Top layer of the surface of the earth" , "Loose upper layer of earth" , "refuse" .)