Wiktionary
wait up
vb. 1 To stay awake waiting for somebody to return. 2 (context colloquial often used in the imperative US English) To wait.
Usage examples of "wait up".
How about if I stay here and wait up for them, and you go with this nice lady here, Xi.
Beggars who die in the streets now have to wait up to two weeks before it's their turn to go.