As in 1 Peter 2:11, the inclusion of this term indicates that Peter is pivoting to a new subject, that is, from the inevitability of suffering to the benefits of suffering. The term itself is a word expressing endearment. Most likely Peter has never met the addressees of this letter. Yet in Christ they are beloved to him (and no doubt he to them).
12 Beloved, do not be surprised at the fiery trial when it comes upon you to test you, as though something strange were happening to you.