Swallowed it in a short time as I was late up (3,2)

I believe the answer is:

ate up

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'swallowed' is the definition.
('eat up' can be a synonym of 'swallow')

'it in a short time as i was late up' is the wordplay.
'ATE UP' is hidden within the letters.
However, I am uncertain how this is indicated.

Can you help me to learn more?

(Other definitions for ate up that I've seen before include "Squandered" , "Absorbed" , "preoccupied" .)

I've seen this clue in the Sydney Morning Herald.

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