Arch rival one in north-eastern canteen (7)

I believe the answer is:

nemesis

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'arch rival' is the definition.
'nemesis' can be an answer for 'rival' (I have seen 'Unbeatable rival ' mean 'nemesis' so perhaps 'rival' could also mean 'nemesis'). I'm unsure of the 'arch' bit.

'one in north-eastern canteen' is the wordplay.
'one' becomes 'I' (Roman numeral).
'in' indicates putting letters inside.
'north' becomes 'N' (synonyms).
'eastern' becomes 'e'.
'canteen' becomes 'mess' (I've seen this before).
'n'+'e'+'mess'='nemess'
'i' placed into 'nemess' is 'NEMESIS'.

Can you help me to learn more?

(Other definitions for nemesis that I've seen before include "Avenging deity" , "Agent of (someone's) downfall" , "Siemens (anag.)" , "Vengeful justice" , "Destiny" .)

I've seen this clue in The Sun.

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