Hi ozbrian
welcome to rootschat

this seems to be the only thomas clarkstone, not a very common surname.
Civil parish: Snenton
Source information: RG10/3504, ed 3, folio 56, page 20
Household schedule number: 133
address: Patent St
Name Age in 1871 Birthplace Relationship occupation
Ann Clarkstone 15 Snenton , Nottinghamshire, England Granddaughter silk winder
Mary Clarkstone 38 Nottinghamshire, England Daughter silk winder
Mary Clarkstone 6 Snenton , Nottinghamshire, England Granddaughter scholar
Sarah Clarkstone 18 Snenton , Nottinghamshire, England Granddaughter silk winder
Thomas Clarkstone 10 Snenton , Nottinghamshire, England Grandson scholar
Ann Woodcock 71 Barton, Nottinghamshire, England Wife
John Woodcock 28 Hyson Green, Nottinghamshire, England Son silk thrower
William Woodcock 71 Barton, Nottinghamshire, England Head F.W.K ??
Mary Clarkstone age 38 is married, John age 28 is unmarried.
No sign of Thomas Clarkestone or a younger brother James.

hope this helps
Tara
