Stick to that light diet (4)
I believe the answer is:
slim
'diet' is the definition.
(both can mean to attempt to lose weight)
I cannot understand how the rest of the clue works.
Can you help me to learn more?
(Other definitions for slim that I've seen before include "Take off weight as by dieting" , "Annual horse race" , "Thin; WWtwo Burma commander" , "to make one lose weight" , "Shed excess weight" .)