Notwithstanding any provisions of this chapter, the Department of Motor Vehicles may grant to any other state, country, territory or district reciprocity with respect to the operation of any vehicles in this State without being registered and licensed under the provisions of this chapter if such other state, country, territory or district extends under its laws, rules and regulations like privileges to vehicles registered and licensed in this State, subject to the conditions that every such vehicle is at all times, when operated in this State, duly registered or licensed in such state, territory, district or country in accordance with the lawful requirements of such state, country, territory or district and that there is displayed thereon a valid registration card and registration or license plate or plates.