This document is about Eleazar (Priest in Ezra's Time). For other homonyms, please refer to the Eleazar document.
He was one of the priests who was with Ezra (the Scribe) during his time.
Ezra 8:33On the fourth day the silver and gold and the vessels were weighed out in the house of our God into the hand of Meremoth the son of Uriah the priest, and with him were Eleazar the son of Phinehas, and with them were the Levites, Jozabad the son of Jeshua, and Noadiah the son of Binnui.
Coincidentally, he is the son of Phinehas.
The Phinehas of Exodus is the son of Eleazar (son of Aaron).