These verses are pretty straightforward. We should obey the governing authorities because God has put these authorities in place over us. When we oppose authority, we oppose and sin against God. If we do good, we have no reason to fear authority. If we do evil, those authorities are in place to avenge us.
Peter wrote about honoring the king who had scattered the Christians throughout the Mediterranean (1 Pet. 2.17). Because of our spiritual freedom, we are not to be rebellious toward the government. We should be law-abiding citizens, so we can claim the protection of the government if charges come against us. In Timothy 2.1-2, Paul charges us to pray for our “kings.” We don’t have to agree with them politically, but we are to pray for them. (See also Titus 3.1)
“The authorities that exist have been established by God.” — Romans 13:1