does polygamy appear only in the Old Testament, or in the New Testament as well?
Both testaments have instances of polygamy. The Bible does not condemn polygamy, but it does definitely limit the leadership of the Church (bishops, elders, and deacons) to those who have only one wife.
Take a look at the men in the Bible who had multiple wives: Abraham, Solomon, David, etc. How did that part of their lives work out?
Abraham: Father of two peoples that hate one another to this day.
David: Led to the rape of Tamar (his daughter) by one of this sons and ultimately a civil war.
Solomon: His many wives turned his heart away from the Lord and led to the worship of other gods in his land.
Those aren't positive outcomes.