We are to submit to every ordinance of man—to the king and the governor. We are to honor all men. Love the brotherhood. Fear God, and honor the king. All of this is seen in the light of two reasons that are given in this context. In verse 16, "but as the servants of God" is reason number one—because we are the servants of God. And, in verse 13, "for the Lord's sake."
I will summarize. Peter is saying that we, as citizens of another Kingdom, living as pilgrims under a government that is not ours—we must never forget who we are! We are servants of the Most High God. We are involved in a spiritual process that is transforming us into the image of Jesus Christ. And government—response to government, and relationships to government—is very important to this process. So, our citizenship is in heaven. We are ambassadors here. We must take these relationships seriously. "For the Lord's sake" means out of regard for Him.