To signal with one's hand for someone or something to continue or proceed through some place or thing. A noun or pronoun can be used between "wave" and "through." The police officer waved through cars at the intersection in lieu of the traffic lights.You'll need to check everyone's ID at the entrance and wave them through if they are supposed to be there.
wave through
v.
To direct or allow someone or something to pass through by or as if by waving the hand or arm: We slowed down at the gate, but the guard waved us through. The customs officials waved through the passengers who had no luggage.