Story overlooking core element in Christmas (4)

I believe the answer is:

noel

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'element in christmas' is the definition.
'Noel' can be an answer for 'christmas' (Noel can mean Christmas). I am not certain of the 'element in' bit.

'story overlooking core' is the wordplay.
'story' becomes 'novel' (I've seen this before).
'overlooking core' says to hollow out the word (remove centre letters).
'novel' with its centre taken out is 'NOEL'.

Can you help me to learn more?

(Other definitions for noel that I've seen before include "Christmas time" , "A lone Christmas in France" , "namely 4 [COWARD]" , "Festive season" , "Coward - Christmas" .)

I've seen this clue in The Independent.

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