wave on

wave on

To signal with one's hand for someone or something to continue or proceed with their current course. A noun or pronoun can be used between "wave" and "on." The police officer waved us on as soon as the other cars had passed through the intersection. We need a team of volunteers to stand at certain parts of the race and wave on competitors so they don't get lost.
See also: on, wave
Farlex Dictionary of Idioms.

wave someone or something on

to make a signal with the hand for someone or something to move on or keep moving. The traffic cop waved us on. The cop waved on the hordes of pedestrians.
See also: on, wave
McGraw-Hill Dictionary of American Idioms and Phrasal Verbs.

wave on

v.
To encourage or signal someone or something to proceed by or as if by waving the hand or arm: The police officer waved the pedestrians on. The crowd waved on the runners.
See also: on, wave
The American Heritage® Dictionary of Phrasal Verbs.
See also:
  • not do (someone or oneself) any favors
  • rescue from
  • rescue from (someone or something)
  • identify with
  • attune to
  • ask back
  • orient
  • orient to
  • orient to (something)
  • involved with