The easier part of the verse is understanding the word for love.
The noun used for the Lord’s love
is אַהֲבָה, not חֶסֶד. The latter, which is the typical word, expresses a love that is seen in the Lord’s unconditional, faithful commitment to his people. The former, the present word, describes a passionate love like that of Jacob for Rachel (Genesis 29:20), Jacob for Joseph (Genesis 37:3), Jonathan for David (Genesis 37:3), and Michal for David (Genesis 37:3). Thus Yahweh’s rejoicing over them can be seen in a marriage metaphor that depicts the reunion of a husband (Yahweh) to his wife (Jerusalem), who have been separated for a period of time.1 His purifying destruction has brought them back into relation with him. His love is one of great intensity, purpose, and delight.2
The harder part of the verse is he will quiet.
The Hebrew verb takes the form of what is normally understood as a causative; hence the ESV’s He will quiet you with his love.
The verb, however, is intransitive in meaning, with the possible exception of Job 11:3. That is, it does not take a direct object, and indeed, here the you
in he will quiet you
is not in the original. The verb in its current form typically “describes the inward condition of the subject of the verb rather than depicting a quietness which is conveyed to another. Here God is the subject of the verb, and he is said to be quiet in his love.”3 The poetic structure of the verse seems to support this; the first and third lines in this final part of the verse contain the phrase over you.
It is common in Hebrew poetry to leave out a corresponding phrase in one line that appears in another line.4 Thus, it is reasonable to regard this same over you
as belonging to the line under consideration: He will be quiet (over you) in his love.
Human actions or human character could never deserve such love. “Zephaniah thus sings the prelude to the cross kind of love Jesus reveals, a love that surpasses knowledge
(Ephesians 3:19). How can this not cause God’s people to praise!"5
17 The LORD your God is in your midst, a mighty one who will save; he will rejoice over you with gladness; he will quiet you by his love; he will exult over you with loud singing.