wait up (for someone) = stay awake at night and wait for someone to come
examples:
- Don 't wait up for me. I won 't come back before midnight.
- I won 't wait up for you, George. I 've got an early morning tomorrow.
- My mum always used to wait up for me.
- What are you doing up so late? I told you not to wait up.
- My parents are too old to wait up for me now. They feel tired and go to bed very early.
