“You are her children, if,” and so forth. Just as the Apostle Paul calls believing Gentiles children of Abraham, the father of believers, according to their faith (Rom 4:16 and parallels), so the Apostle Peter calls women who believe in Christ children of Sarah. This means according to faith and according to the spirit. It was considered a great honor, especially for Jewish women.
“If you do good”: this means not only obedience to husbands, of which the Apostle is directly speaking, but a virtuous life in general. He had exhorted all to such a life above (1 Pet 2:12). In general, we see that he interweaves particular instructions with general ones, rising from the former to the latter and descending back again.
“And are not frightened by any fear”: whether this be fear caused by unbelieving husbands in believing wives, through misunderstandings about faith and conduct, or fear from the unbelieving world generally, in its hostility against Christianity.
With hope in God, such as the holy women had (1 Pet 3:5), and with a virtuous, pure, and God-fearing life (1 Pet 3:2), no fear should have any place in their soul. It should not disturb their hidden man in the incorruptible beauty of their meek and quiet spirit (1 Pet 3:4), wherever such fear might come from.
Blessed Theophylact gives yet another interpretation of the words “do not be frightened by any fear”: “While urging them toward adornment fitting for Christian women, he also persuades them to be merciful, without fearing a reckoning from their husbands. For this is what he wishes to express by the words: ‘do not be frightened by any fear.’ It is natural that husbands may sometimes demand from them an account of expenses. By such lofty speech, the Apostle persuades thrifty and fainthearted women to distribute household goods more generously. He also restrains husbands from severity” (Theophylact).