One eating no fat fish (5)
I believe the answer is:
sprat
I believe this clue is a double definition.
'one eating no fat' is the first definition.
('Jack Sprat could eat no fat' in the nursery rhyme)
'fish' is the second definition.
(sprat is a kind of fish)
(Other definitions for sprat that I've seen before include "Young herring" , "Couple sharing meat" , "chap giving richer course material to the Dutch" , "Traps (anag.)" , "Small sea fish" .)