With the designation “elder” Peter is describing himself as an older person of such standing as to be expected to give leadership. As a “fellow” elder he places himself beside the leadership among his readers. Though he has earlier described himself as “an apostle of Jesus Christ” (1 Peter 1:1), he is now removing any sense of superiority or suggestion that he is speaking down to these elders. Instead, he positions himself as one of them, and so as a man who knows the struggles that come with being an elder. This self-designation will make the task description he will provide in coming verses more palatable since he is asking nothing from them that he is not asking of himself (and that will include an eventual martyrdom). It should be noted that Acts 15:2, Acts 15:4, and Acts 15:6 mention “apostles” and “elders” as two groups. That does not necessarily imply that the apostles were not seen as “elders” in the (church) circles where they gravitated toward. It does imply that they were more than “elders”; they were also “apostles.”
1 So I exhort the elders among you, as a fellow elder and a witness of the sufferings of Christ, as well as a partaker in the glory that is going to be revealed: