If you are talking about the film, no-one has been able to figure out what the political situation is there.
In the
books Isildur and his brother Anardil were the co-kings and founders of
Gondor while their father
Elendil founded the northern kingdom of
Arnor.
After Elendil and Anardil were killed in the
War of the Last Alliance, Isildur as the eldest son of Elendil, took for himself the kingship of Arnor and had his nephew, Meneldil son of Anardil, made
King of Gondor.
The line continued to King Ondoher.
But when Ondoher King of Gondor and his two sons were slain there was no clear heir to the throne. At that time King Avedui of Athedain descendant of Isildur put in a claim. But Arvedui was rejected in favor of Ondoher’s distant cousin Eärnil. Eärnur his son later succeeded to the throne, but foolishly answered a challenge to personal combat from the
Lord of Minas Morgul and was never heard of again.
At this point the line of the
kings of Gondor descended from Meneldil was broken.
Now the descendants of the kings had become few. Their numbers had been greatly diminished in the Kin-strife; whereas since that time the kings had become jealous and watchful of those near akin. Often those on whom suspicion fell had fled to
Umbar and there joined the rebels; while others had renounced their lineage and taken wives not of Númenorean blood. So it was that no claimant to the crown could be found who was of pure blood, or whose claim all would allow; and all feared the memory of the Kin-strife, knowing that if any such dissension arose again, then Gondor would perish. Therefore, though the years lengthened, the Steward continued to rule Gondor, and the crown of Elendil lay in the lap of King Eärnil in the Houses of the Dead, where Eärnur had left it.
Meanwhile the kingdom of Arthedain had also fallen and Arvedui with it. Arvedui’s son Aranarth took on himself only the title of Chieftain of the
Dúnedain of the North. Aranarth had a reasonable claim to the throne of Gondor, but presumably was also one of those whose claim not all would allow (and he had no power to push it by force even if he had wished to do so). No-one wanted civil war.
Accordingly the
Stewards ruled until Aranarth’s descendant
Aragorn claimed the throne after saving the
city of
Minas Tirith.
We are not told whether there were any descendants of Minardil still about when Aragorn made his claim who might also have had some degree of valid claim.