Mountain woman in the first place needs sleep (7)

I believe the answer is:

everest

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'mountain' is the definition.
(Mount Everest)

'woman in the first place needs sleep' is the wordplay.
'woman in the first place needs' becomes 'eve' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'sleep' becomes 'rest' (synonyms).
'eve'+'rest'='EVEREST'

Can you help me to learn more?

(Other definitions for everest that I've seen before include "Mountain named after a British surveyor general of India" , "High mountain" , "Highest Himalayan mountain" , "Himalayan mount" , "High peak" .)

I've seen this clue in The Times.

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