Stay the night and get up late, if reversed (5,4)

I believe the answer is:

sleep over

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'stay the night' is the definition.
(I've seen this before)

I don't understand how the remainder of the clue works.

(Other definitions for sleep over that I've seen before include "stay the night" , "A night away from home" , "Night at another (child's) house" , "as a result of 25 [REVEILLE]?" , "Remain for the night" .)

I've seen this clue in The Mirror.

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