Jeshua (Haggai 1:1; Zechariah 3:1) was the high priest (Nehemiah 12:1). However, Ezra did not use this title (Ezra 2:2; 3:2; 4:3; 5:2), which suggests the title was given after the temple was completed (6:15).
Zerubbabel served as the governor of Judah, appointed by Persia (Haggai 1:1), likely after Sheshbazzar died (see study note on Ezra 1:8). He was the grandson of King Jehoiachin of Judah (1 Chronicles 3:17).