Now, we are going to cover v8-10. Verses 1-7 that we just covered appear rather abruptly considering Romans chapters 1-12. Those chapters flow nicely together. But Romans 13:1-7 seem out of place. But I think those 7 verses have been inserted intentionally to set the stage to introduce the meat of this chapter which starts in v8.
The people in authority are giving their full time to governing. And in the same way that Paul is called to preach to the Gentiles, these politicians are equally called by God to be His servants in the political arena. And the principle is clear — give them what they are due. Pay your taxes.
And we see Paul applying this concept in a broader sense in v7 because he says —
7 Give [not just your ruling authorities but give] EVERYONE what you owe him: If you owe taxes, pay taxes; if revenue, then revenue; if respect, then respect; if honor, then honor.