9:33a Those who were musicians, the heads of Levite families,

Some descendants of Levi who were leaders in their clans/families were musicians/singers.
-or-
Some men from the clan of Levi were musicians and chiefs in their clans.

9:33b stayed in the temple chambers and were exempt from other duties

They stayed in the temple rooms and were free from other duties
-or-
They lived in the rooms for the workers in the house of God. They did no other work

9:33c because they were on duty day and night.

because they were in charge of the music. Their work/service as musicians continued day and night.
-or-
except the worship music. Their work duties took place during the day and at night.
-or-
They had to be available to perform their music/service day and night.

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