The executive, Jeffrey McConney, has long served as the Trump Organization’s controller, making him one of a handful of high-ranking executives to oversee the company’s finances. The testimony comes as the prosecutors have trained their focus on one of Mr. McConney’s colleagues, Allen H. Weisselberg, the Trump Organization’s long-serving chief financial officer. The prosecutors, who are working for the Manhattan district attorney, Cyrus R. Vance Jr., have examined the extent to which Mr. Trump handed out valuable benefits to Mr. Weisselberg’s family and whether taxes were paid on those perks, The New York Times has reported. Mr. Vance’s office has mounted an aggressive effort to gain Mr. Weisselberg’s cooperation against Mr. Trump and the Trump Organization, people with knowledge of that effort have said. When seeking to turn an insider into a cooperating witness, prosecutors often seek leverage over the person, including any evidence of past wrongdoing, and then typically offer leniency in exchange for testimony or assistance.