One should not eat more quickly (6)
I believe the answer is:
faster
This clue is a double definition.
'one should not eat' is the first definition.
(to fast is to refrain from eating food)
'more quickly' is the second definition.
(synonyms)
(Other definitions for faster that I've seen before include "More rapid" , "Lent Observer" , "with more security" , "Speedier" , "more rapidly" .)