Nehemiah 11:22 shows the sons of Asaph still serving as singers in Jerusalem, continuing the tradition.

1 Chronicles 25:1-31 gives the full account of David and Asaph appointing singers, which Nehemiah 12:46 summarizes.

2 Chronicles 29:30 shows Hezekiah restoring songs of David and Asaph, continuing the tradition Nehemiah 12:46 references.

1 Chronicles 6:39 gives the genealogy of Asaph, the singer appointed by David mentioned here.

1 Chronicles 15:16 describes David appointing Levite singers, the very origin of the practice mentioned here.