Every now and then Aztecs ate relish (4)
I believe the answer is:
zest
'relish' is the definition.
(I know that relish can be written as zest)
'every now and then aztecs ate' is the wordplay.
'every now and then' means one should take alternating letters (letters selected at regular intervals).
'aztecs'+'ate'='aztecsate'
The alternating letters of 'aztecsate' are 'ZEST'.
(Other definitions for zest that I've seen before include "Peel used as flavouring" , "Great energy; citrus peel" , "bit of a lemon" , "Zing" , "added flavour" .)