Gov. Chris Christie of New Jersey offered a glimpse Monday of just what he might bring to the Republican ticket as Donald J. Trump’s running mate, presenting himself as a law and order executive in an appearance with Mr. Trump in Virginia Beach.

Speaking for nearly eight minutes before Mr. Trump gave his own remarks, Mr. Christie joined the growing list of Republicans — including both Senator Bob Corker of Tennessee and Newt Gingrich last week — to appear alongside Mr. Trump as he works to select his No. 2 in a public auditioning evocative of his reality television show, “The Apprentice.”

After the racially charged tragedies that have roiled the nation — the assassination of five Dallas police officers by a sniper and the killing of black men by police officers in Louisiana and Minnesota — Mr. Christie spoke forcefully about “safety and security” as the two greatest issues facing the country.

“We need a president who once again will put law and order at the top of the priority of the presidency of this country,” Mr. Christie said. “We need once again to have a president who puts the safety and security of our citizens first and does not blink or hesitate to take the strong action that needs to be taken to make sure that those both at home and around the world know that lawlessness will not be tolerated from anyone.”