The granddaughter of his brother Robert Clavering (1625–1675) (who had married the heiress to the estate at Chopwell Hall, Chopwell, Co Durham) married William Cowper, 1st Earl Cowper in 1706. Their son William changed his name to Clavering-Cowper on inheriting Chopwell from his uncle.
Clavering married Jane Maddison in 1640. Three grandsons in turn succeeded to the Baronetcy; James, John, and Francis.