Stick to that light diet (4)

I believe the answer is:

slim

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'diet' is the definition.
(both can mean to attempt to lose weight)

I can't explain the rest of the clue.

(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" .)

I've seen this clue in the Evening Standard.

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