The convention has always been for higher degrees in the peerage not to include the territorial designation, however many times the peerage is recreated. See below the link to the obit in today's Telegraph (28 April):
Countryman and conservationist who transformed the fortunes of his family’s Norfolk estate
Edward Douglas Coke was born in Southern Rhodesia (now Zimbabwe) on May 6 1936, the eldest son of Anthony Coke, the son of a younger son of the 3rd Earl of Leicester (who had been killed at Gallipoli) by Moyra Crossley, the first of his three wives. ….
Edward spent much of his childhood on a remote farm in South Africa with no electricity…. After leaving St Anthony’s College, Grahamstown, he worked for a veterinary pharmaceutical company followed by an agricultural research organisation.
Neither he nor his father had much expectation of inheriting the earldom. However the 5th Earl had daughters but no sons and by the 1960s it was clear that his cousin Anthony would inherit the title and the Holkham estate.
As the next in line, Edward Coke came to England at the age of 26 and settled in the Holkham area in order to take up farming and familiarise himself with the estate, taking over its management in 1973. In 1976, following the death of the 5th Earl, his father became the 6th Earl but chose to remain in South Africa, so Edward, as Viscount Coke, took over the full responsibility for the leadership as well as the management of the estate. He became the 7th Earl of Leicester on his father’s death in 1994….
Edward Coke married, first, in 1962, Valerie Potter. The marriage was dissolved in 1985 and the following year he married, secondly, Sarah de Chair (née Forde), who survives him with the daughter and two sons of his first marriage….