Drúwaith Iaur was not a part of the realm of Gondor, and therefore also not of the Reunited Kingdom. It was the original home of the Drúedain, the original inhabitants of the Ered Nimrais, who were dispersed by the Númenóreans as they were hostile to them.
Drúwaith Iaur is a Sindarin name, consisting of drú ("wild") + waith ("folk, land") and iaur ("old"); it is thus a literal translation of Old Púkel land. On a "scrap of writing", according to Christopher Tolkien, the word Iaur did not mean "original" but "former".
Other versions of the legendarium
In his essay about the Drúedain, J.R.R. Tolkien says that the region east of the Mountains, in Anorien, was believed to be the home of the remnants of the Drúedain, called "the Old Pukel-wilderness (Druwaith Iaur)" by the Gondorians,:p. 384 obviously referring to the Drúadan Forest. However in A Map of Middle-earth, he indicated the coastal land west of Gondor to Pauline Baynes:p. 387, Note #13 indicating this time their original homeland.
- J.R.R. Tolkien, Christopher Tolkien (ed.), Unfinished Tales, "The West of Middle-earth at the End of the Third Age" [map]
- J.R.R. Tolkien, "The Rivers and Beacon-hills of Gondor" (edited by Carl F. Hostetter), in Vinyar Tengwar, Number 42, July 2001, p. 9
- J.R.R. Tolkien, Christopher Tolkien (ed.), Unfinished Tales, "The Drúedain"
- Wayne G. Hammond and Christina Scull (eds), The Lord of the Rings: A Reader's Companion, p. lxiv