In point of fact Peter does not mention the word emperor at all. Instead, he uses the word for king, without the definite article the. In relation to this term, note the following.

As Roman armies conquered territory, they commonly did not dismantle but retained the authority structures that were already in place. That includes retaining monarchies and kings, though those kings from now on were accountable to their Roman overlords. Understandably, conquered tribes commonly had warmer feelings toward their king (typically one of their own) than toward the foreigners to whom their king now had to give account (and taxes). From sources outside the Bible we are aware that in the regions in which Peter’s readers lived (see 1 Peter 1:1) there remained monarchies—kings—that the Romans retained. Irrespective of how you felt about a particular king (he was a finite creature and in your judgment incompetent and his policies wrong), Peter’s instruction was that his readers were to consciously acknowledge their place under this king.

By placing themselves willingly under this human creature, Peter’s readers were by extension also to place themselves under their king’s overlord. In Peter’s day that was most likely Caesar Nero. At what time Nero’s narcissism and pedophilia became known to the locals of far-flung provinces as Pontus, Galatia, Cappadocia, Asia, and Bithynia is unknown. Even so, the Holy Spirit moved Peter to instruct these sojourners and exiles—on their way to the Promised Land—to embrace Nero as the man God himself was pleased to place at the top of society’s hierarchal ladder as his tool to govern the nations.

Peter had used the same word (king, here translated as “emperor) a few verses earlier to describe his readers. Though they were exiles (1 Peter 1:1, 1 Peter 1:17), they were in fact by God’s grace “a royal priesthood” (1 Peter 2:9). They should see themselves as kings (with Christ, Ephesians 2:6) whose style of kingship (like Christ’s during his earthly sojourn, Matthew 21:5; Matthew 27:37) is cloaked in humility.