Mounting school bill? (4)

I believe the answer is:

eton

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This could be a double definition.

'mounting' is the first definition.
Both the definition and answer are singular nouns.
Perhaps you can see an association between them that I can't see?

'school bill?' is the second definition.
'eton' can be an answer for 'school' (famous UK public school). I'm not certain of the 'bill?' bit.

Can you help me to learn more?

(Other definitions for eton that I've seen before include "School - note (anag)" , "Noted public school" , "Posh British public school" , "British public school of note" , "Public school (sounds like 20)" .)

I've seen this clue in The Globe and Mail.

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