Discourage careful eater, second to quit (5)
I believe the answer is:
deter
'discourage' is the definition.
(synonyms)
I cannot understand how the rest of the clue works.
Can you help me to learn more?
(Other definitions for deter that I've seen before include "Discourage through fear of consequences" , "'Discourage, dissuade (5)'" , "Hinder, discourage" , "Put (someone) off" , "Discourage or prevent from doing something" .)