When Aragorn became King of Gondor at the end of the War of the Ring, he was also the descendant of the Kings of Arnor, and by right he was crowned High King of both Arnor and Gondor and Reunited the Two Kingdoms, which had politically split long ago. Using the resources of the victorious Gondor, Aragorn, taking the royal name King Elessar, rebuilt Arnor in the North.
With the defeat of Sauron and Mordor, the Reunited Kingdom of Aragorn was without question the dominant power of Northwest Middle-earth during his long reign.
During Aragorn's reign, the Reunited Kingdom expanded to retake all territories that had originally belonged to both Arnor and Gondor at their greatest extents, excluding only Rohan (the grant of which he renewed), and the Shire, the Druadan Forest, and Fangorn Forest (which became protectorates).
Additionally, during the 1st century of the Fourth Age Aragorn led the armies of the Reunited Kingdom in many successful military campaigns that retook the province of South Gondor (Harondor), re-established dominance over Rhovanion (Wilderland) eastwards to the Sea of Rhûn, and conquered the Corsairs of Umbar, who had attacked Gondor during the War of the Ring. Umbar had originally been a Númenórean port and an important city of Gondor in ancient times before ultimately being conquered by the followers of Castamir following the Kin-strife, who distanced Umbar from Gondor and befriended Harad. Elessar finally reconquered the city, and the Reunited Kingdom stretched South along the coast from the Mouths of the Anduin River to the Haven of Umbar. Much of Harad was defeated and became tributary states. Aragorn was also held to be the protector of Dale (which included Esgaroth), and the Dwarf realm of Erebor, although these allies maintained their own rule and kings. Aragorn is assumed to have rebuilt the old northern capital of Annúminas.