Incline to being with little fat (4)
I believe the answer is:
lean
I believe this clue is a double definition.
'incline' is the first definition.
(I know that incline is a kind of lean)
'with little fat' is the second definition.
(I've seen this before)
'to being' acts as a link.
(Other definitions for lean that I've seen before include "Slant" , "Spare - list" , "Inclination" , "Tend towards being thin" , "Incline to prop against" .)