Elvis act jazzed up Elvis's no. 1? We must accept it (4,2,3)

I believe the answer is:

cest la vie

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'we must accept it' is the definition.
I can't judge whether this definition defines the answer.

'elvis act jazzed up elvis's no 1?' is the wordplay.
'jazzed up' is an anagram indicator.
'elvis's no 1?' becomes 'e' (1st letter of 'elvis').
'elvis'+'act'='elvisact'
'elvisact' anagrammed gives 'cestlavi'.
'cestlavi'+'e'='CEST LA VIE'

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(Other definitions for cest la vie that I've seen before include "There's nothing we can do about it!" , "Whatever will be will be" , "Vets Alice (anag) - French expression of resignation" , "That's life for the French (1'3,2,3)" .)

I've seen this clue in The Times.

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