Definition of wait up phrasal verb from the Oxford Advanced American Dictionary

 

wait up

 phrasal verb
phrasal verb
 
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Phrasal Verbs
used to ask someone to stop or go more slowly so that you can join them Wait up — you're walking too fast for me.

wait up (for somebody)

 
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to wait for someone to come home at night before you go to bed I'll be back very late, so don't wait up for me.
See the Oxford Advanced Learner's Dictionary entry: wait up