Carefully gets by Speke - so utterly captivating (4,3)

I believe the answer is:

ekes out

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'carefully gets' is the definition.
I don't know anything about this answer so I can't judge whether this works.

'speke so utterly captivating' is the wordplay.
'EKES OUT' is hidden in amongst the letters.
However, I'm uncertain how this is indicated.

'by' acts as a link.

Can you help me to learn more?

I've seen this clue in The Independent.

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