Before hiring Mr. Fischetti, people close to Mr. Trump and the Trump Organization had reached out to lawyers in New York for recommendations or to discuss representing the former president or his company, people familiar with the matter said. Some of the people who received calls were former prosecutors in the Manhattan district attorney’s office, and many had a reputation for being aggressive advocates, the people said. Mr. Fischetti, a partner at the Fischetti and Malgieri LLP firm, has spent decades as a defense attorney working in both state and federal courts. His prior clients include former South Carolina State Sen. Albert Carmichael Jr., who was convicted of buying votes during a 1980 Democratic primary; and former U.S. Rep. Robert Garcia and his wife, whose 1989 public-corruption convictions were overturned.