Romans 13 and 1 Peter 2 are both used to teach that we must always obey any and all government rules. Sometimes an exception is made allowing for laws that violate scripture. I will not get into all the issues. My only goal is to teach the meaning of scripture.
Romans 13:1-4 "Let every soul be in subjection to the higher authorities, for there is no authority except from God, and those who exist are ordained by God. Therefore he who resists the authority, withstands the ordinance of God; and those who withstand will receive to themselves judgment. For rulers are not a terror to the good work, but to the evil. Do you desire to have no fear of the authority? Do that which is good, and you will have praise from the same, for he is a servant of God to you for good. But if you do that which is evil, be afraid, for he doesn't bear the sword in vain; for he is a servant of God, an avenger for wrath to him who does evil."
Romans 13:4 should make the intent of this section obvious, but this is the key to verse one. The governing authority is one that supports God's Law and makes those who do evil afraid.
G1849: From G1832 (in the sense of ability); privilege, that is, (subjectively) force, capacity, competency, freedom, or (objectively) mastery (concretely magistrate, superhuman, potentate, token of control), delegated influence
It does take some digging in the Greek, but if you notice that the root of power or authority is rooted in "I exist" or "I AM".
So the Law that is being discussed and in use by the authorities is the Law of I AM. Only Yahweh God's Law is being discussed. Here is a five minute excerpt from a lesson by a friend from many years ago. Concentric Authority - Eric Benson.
One more aspect is found in the word "from" in the phrase "for there is no authority except from God". Strong's Concordance shows the Greek word as "apo" meaning from. The actual Greek text though has "upo" which is under. This means that any man made "authority" making its own law has removed itself from under God's authority and is rejecting Yahweh's authority and perfect Law.
1 Peter 2:13-14 "Therefore subject yourselves to every ordinance of man for the Lord's sake: whether to the king, as supreme; or to governors, as sent by him for vengeance on evildoers and for praise to those who do well.".
The word ordinance is the word we will look at here.
G2937: From G2936; original formation (properly the act; by implication the thing, literally or figuratively)
This one is a bit harder to see, but the reference is there to the original formation, the proprietor, God. Regardless, the government indicated is one that punishes evildoers and praises the righteous. These terms must be understood in light of God's Law. Scripture would never give support to any government who rewards evil and condemns the righteous.
There are two mentions in the word of God that have any apparent support for man's government. One is Christ's "render to Caesar" and with the phrase "Give therefore to everyone what you owe" referring to taxes and customs in Romans 13:7. This is true. If it is due and if you owe it, you should pay it.
Feel free to send your helpful comments.