Which high priest did Haggai address together with Zerubbabel?

Answer: Joshua son of Jehozadak

Haggai spoke to Joshua son of Jehozadak, the high priest, telling him and Zerubbabel, "Be strong... for I am with you."

“In the second year of the reign of Darius, on the first day of the sixth month, the word of the LORD came through Haggai the prophet to Zerubbabel son of Shealtiel, governor of Judah, and to Joshua son of Jehozadak, the high priest, stating”— Haggai 1:1 (BSB)