Get fruit via supermarket loyalty scheme in mid-September (9)

I believe the answer is:

nectarine

I'm a little stuck... Click here to teach me more about this clue!

'get fruit via supermarket loyalty' is the definition.
I can't judge whether this definition defines the answer.

'scheme in mid-september' is the wordplay.
'scheme' becomes 'nectar' (I can't explain this - if you can you should give a lot more credence to this answer).
'mid' says to take the centre (mid- can mean the middle of something).
'september' becomes 'sep' (short for September).
The middle of 'sep' is 'e'.
'nectar'+'in'+'e'='NECTARINE'

Can you help me to learn more?

(Other definitions for nectarine that I've seen before include "fruity" , "Fruit - aren't nice (anag)" , "Variety or mutation of a peach" , "Kind of peach with thin skin and no down" , "Peach-like fruit" .)

I've seen this clue in The Independent.

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