Cleveland was a county in North East England between 1974 and 1996, straddling the River Tees. It was then abolished and its towns re-assigned.
Towns to the north were re-assigned to County Durham. These are Hartlepool and Stockton-on-Tees. Stockton also straddles the river, and governs the southern rural district of Yarm even though that's in a separate county.
The Cleveland Hills, and the Cleveland Way long-distance footpath, are in North Yorkshire.