Name given at incorporated on 23 May 1828 to honour the Duke of Clarence, later King William IV. The line was leaved to the Stockton and Hartlepool Railway from 22 September 1844 for 21 years, and in perpetuity with effect from 1 January 1851, but was absorbed by the West Hartlepool Harbour and Raliway on 30 June 1852.