Gain fame at last, plugging a food flavouring (7)

I believe the answer is:
achieve
'gain' is the definition.
(I've seen this before)
'fame at last plugging a food flavouring' is the wordplay.
'at last' suggests the final letters.
'plugging' indicates putting letters inside (inserted letters plug up a gap in the word).
'food flavouring' becomes 'chive' (I can't explain this - if you can you should believe this answer much more).
The final letter of 'fame' is 'e'.
'a'+'chive'='achive'
'e' going within 'achive' is 'ACHIEVE'.
Can you help me to learn more?
(Other definitions for achieve that I've seen before include "Bring about by effort" , "wrap up" , "Accomplish, gain by effort" , "Finish" , "Successfully bring off" .)