To avoid relegation, don't have early nights! (4,2)

I believe the answer is:

stop up

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'to avoid' is the definition.
Although both the answer and definition are verbs in their base form, I can't understand how one could define the other.

I don't understand the rest of the clue.

Can you help me to learn more?

(Other definitions for stop up that I've seen before include "Block (eg an earth)" , "close" , "Cork" , "Don't go to bed early" , "Don't retire here" .)

I've seen this clue in the Evening Standard.

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