Paramount honcho Brad Grey closed on a $15.5 million apartment in the Carlyle Hotel last week. The 4-bedroom, 3,000-square-foot condominium, which includes a library, spreads across the entire 26th floor of the iconic hotel. Grey bought the place from asset manager Peter M. Schoenfeld, who reportedly purchased the condo for under $6.5 million in 2007. “It’s a second home for Grey,” a source said. “He’s stayed at the Carlyle for years. His primary residence will be in Los Angeles.” Grey has two homes in LA, including Frank Sinatra’s former residence in Holmby Hills, which he bought for $18.5 million in 2010 but listed last September for $23.5 million.