Flavouring also stays with you! (7)
I believe the answer is:
aniseed
'flavouring' is the definition.
(I've seen this before)
'also stays with you' is the wordplay.
'also' becomes 'and' (both can mean in addition).
'stays' indicates putting letters inside (\'stay\' could historically mean restrain or curb).
'with you' becomes 'isee' (I can't justify this - if you can you should give a lot more credence to this answer).
'and' placed around 'isee' is 'ANISEED'.
Can you help me to learn more?
(Other definitions for aniseed that I've seen before include "Flavouring in pastis" , "Plant" , "Liquorice flavour" , "Flavouring of e.g. absinthe" , "Strong flavour" .)