Pelendur helped Gondor through a constitutional crisis following the premature death of King Ondoher and his heirs in battle. He effectively ruled the kingdom for one year while observing the claims of the two claimants, Prince Arvedui of Arthedain and the general Eärnil who was victorious in battle against the Wainriders (Easterlings).
Pelendur dismissed Arvedui's claim maintaining that the rule of Gondor belonged to the heirs of Anarion, even though Isildur was the High King of both Gondor and Arnor before his death. Arvedui also argued, his wife Fíriel, the daughter of Ondoher should rightfully become Ruling-Queen due to the old Númenorean law of accession, which stated the eldest remaining child of the King should inherit the throne. Pelendur rejected Fíriel's claim saying in Númenor, it was peaceful enough to have women as rulers. However, the Realms-in-Exile were constantly under attack and therefore needed a male ruler to lead the armies.
Based on the afore-mentioned data the Council of Gondor, under the influence of Pelendur, threw out Arvedui's claim and chose Eärnil as King, defying the Númenorean law of succession, which was said to be unappliable in a warring state like Gondor. Although Pelendur's choice denied the heirs of Isildur to re-unite the Realms-in-Exile, it may have averted another kin strife. Eärnil, the victorious general, had become a hero in Gondor and had the support of the populace for his deeds in battle. Installing Arvedui, a foreigner, as king could have stirred up resentment amongst the people of the coastlands and the supporters of Eärnil, who had saved Gondor.
This political precedent (choosing a Gondorian rather than an heir of Isildur with a more direct claim to the throne) is one reason for Aragorn's caution in assuming the throne of Gondor at the end of the Third Age.