From chieftain +‎ -ship.

chieftainship (countable and uncountable, plural chieftainships)

1. (uncountable) The state of being a chieftain
   • 1852 Commission to Inquire into the Past and Present State of the Kafirs

     Shortly after the death of his father, Chaka obtained the chieftainship of the Zulu nation, through the influence of his patron.

   • 1941 February, O. S. Nock, “The Locomotives of Sir Nigel Gresley: Part 1—G.N.R. 1911-1914”, in Railway Magazine, page 77:

     First as Locomotive Superintendent of the Great Northern Railway, and then as Chief Mechanical Engineer of the L.N.E.R., his chieftainship bridges not merely 28 years of great events in the railway world, but has also witnessed a complete transition from the old operating methods, when engines were nursed and groomed like racehorses, to the stringent economic conditions of today.

2. (countable) The area ruled by a chieftain
   • 1847, Henry Rowe Schoolcraft, The Red Race of America:

     They exist in chieftainships, each head of which has his own local jurisdiction, civil and criminal.

• “chieftainship”, in Lexico, Dictionary.com; Oxford University Press, 2019–2022.