You're right, the Old Testament was a preview on the New Testament to all times, so priests were a preview for the Messiah and ok in that time, till the moment when Jesus Christ comes to become our high priest in heaven (Hebrews 4:14), that makes humanly priests unnecessary.

When I think about it, it's even profane to call humans priests and to ignore "Hebrews 4:14-16" on that way, so thanks for to rebuke me @elizahfhaye what's biblical too (2. Timothy 4:2).