NAB shuts several NSW branches 30 June 2009 4:56PM National Australia Bank confirmed to the Herald Sun that it was closing several branches in New South Wales. Suburban branches being closed in NSW include those at Pennant Hills, Silverwater, Turramurra and Menai. One city branch in Clarence St will also close.The bank shut at least eight branches in Victoria earlier this year, according to the newspaper, as a part of a wider program of closing up to 35 branches from its network.