After entering private practice Claiborne quickly became a well-known defense attorney in Las Vegas. Claiborne not only represented many police officers in legal matters without charge, but helped establish the police protective association in Las Vegas and was instrumental in securing the passage of legislation providing for civil service status for policemen and firemen by the Nevada legislature. He was considered one of Nevada's top defense lawyers, representing many prominent people with ties to Las Vegas. Frank Sinatra and Dean Martin hired him for casino licensing matters. Judy Garland, Carol Burnett, and one of Errol Flynn's wives came to him for divorces. He represented several mobsters like Bugsy Siegel and Frank "Lefty" Rosenthal. He also represented Giuseppe "Joe" Conforte, the owner of the Mustang Ranch brothel, and Benny Binion, owner of the Horseshoe Casino. All his clients, whoever they were, were advised not to fill out financial net worth statements when applying for gaming licenses; Claiborne said these could be used as evidence in possible income tax evasion prosecutions by the IRS. He said he personally would never fill one out. Claiborne was a flamboyant attorney who would frighten other lawyers by carrying in large stacks of papers that he passed off as his evidence in the case, but in reality the papers in the folders often were blank. In 1974 and 1975 Claiborne served as a special assistant to the United States Senate Committee on Rules and Administration during the historic hearings on Nelson Rockefeller's nomination to the vice-presidency.