http://devotional.prophecytoday.com/2018/03/zechariah-612.html
The key to this passage is noticing that the Branch will have a throne, will be a priest, and will be peace (Zechariah 6:13). A throne means a civil ruler like Zerubbabel (in Zechariah’s day), a type of David. A king was forbidden from being a priest (StackExchange notes the priesthood was restricted to Levi, while the kingship was restricted to Judah). Uzziah as king attempted to offer a sacrifice (2 Chronicles 26:16), and was cursed with leprosy (2 Chronicles 26:19-21).
What Prophesied Man could be both King and Priest? The Branch is The Peace – and as we showed earlier, that is Jesus! In the Milllennium He will build the Ezekiel Temple.