Crossword Genius

Whatever happens, they'll supply this, no matter what price they get? (2,3,4)

Ross

I believe the answer is:

at any rate

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'whatever happens' is the definition.
('at any rate' means whatever the outcome)

'they'll supply this no matter what price they get?' is the wordplay.
I cannot really understand how this works, but
'no' could be 'n' (common abbreviation) and 'n' is present in the answer.
'matter' could be 'te' (Te is an example) and 'te' is located in the answer.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?

(Other definitions for at any rate that I've seen before include "Price thus unspecified" , "Nevertheless" , "if nothing else" , "come what may" , "Anyhow, anyway" .)

I've seen this clue in The Irish Times.
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