Most evangelicals understand the author of 1 Peter (and so the author behind 1 Peter 1:13) to be the Apostle Simon Peter. Below is a concise evangelical summary about him and why he is regarded as the likely author.

Who he was
– Simon (son of Jonah/Jonas), a Galilean fisherman from Bethsaida, brother of Andrew. Jesus gave him the name Cephas (Peter, “rock”).
– An early, prominent disciple: he confessed Jesus as the Messiah (Matt 16), was present at the Transfiguration and Gethsemane, and was a leader in the Jerusalem church.
– Character: impetuous and bold, yet deeply devoted; denied Jesus and was later restored by Him (John 21), which shaped his pastoral heart for repentant and suffering Christians.
– Traditional later ministry: active among Jewish and Gentile Christians, widely associated with ministry in Rome; tradition holds he was martyred under Nero (mid-late AD 60s), reportedly crucified.

Why evangelicals accept Petrine authorship
– Internal claim: the letter opens by identifying its writer as “Peter, an apostle of Jesus Christ” (1:1), which evangelicals take at face value unless good reason exists to deny it.
– Early church testimony: several early Christian writers (e.g., Clement of Rome, Irenaeus, Clement of Alexandria, Tertullian) accepted 1 Peter as Peter’s letter, and church tradition links Peter with Rome (1 Peter 5:13’s “Babylon” is often understood as a cryptic reference to Rome).
– Style explained by circumstances: 1:1 and other places indicate Peter wrote “through” or “with” Silvanus (Silas) — evangelicals understand Silvanus as an amanuensis or associate who could have helped shape the Greek and the letter’s polish.
– Theological and experiential fit: the letter’s emphases — witness of Christ’s suffering and of his coming glory, pastoral exhortation to holiness amid suffering, and the urgency of apostolic authority — fit well with Peter’s known life and role as an eyewitness apostle.

Context of 1 Peter 1:13 (brief)
– The verse urges believers to “prepare your minds for action; be sober-minded; set your hope fully on the grace to be brought to you at the revelation of Jesus Christ” (paraphrase). In the letter’s context Peter is calling Christians to holiness, mental readiness, and hope while they face suffering and social pressure.
– Because Peter writes as an eyewitness and apostle, his exhortations carry pastoral weight for churches under trial; evangelicals see the verse as practical apostolic instruction grounded in apostolic authority.

Caveat (noting scholarly difference)
– Some critical scholars question direct Petrine authorship because of the letter’s polished Greek and certain theological developments. Evangelicals typically respond that (1) Peter could have used a skilled amanuensis (Silvanus), (2) educated Jews from Galilee could attain good Greek, and (3) the letter’s apostolic perspective and early acceptance argue for genuine Petrine origin.

Pastoral application (short)
– From an evangelical viewpoint, 1 Peter 1:13 reflects an apostle’s urgent call: believers are to discipline their thinking, live soberly, and anchor their hope in Christ’s promised revelation — especially timely for Christians living faithfully amid suffering.

If you’d like, I can summarize documentary evidence from early church fathers, explain the role of Silvanus in more detail, or give a verse-by-verse look at the chapter from a conservative evangelical commentary.