1 Chronicles 23:24-27 is arranged chiastically:
A. Levites numbered from 20 years and up.
B. David said.
C. Yahweh rests and dwells.
C'. Levites no longer carry tent and implements.
B'. Words of David.
A'. Levites numbered from 20 years and up.
C' is disputable, but the structure nearly forces us to make a connection between David's declaration about Yahweh and the change in the Levites' responsibilities. The import is: Yahweh has entered rest and given rest to His people; the Levites are the primary recipients of that rest; instead of the back-breaking work of carrying the tabernacle from place to place, they have been given a “standing” (v. 28, ‘amad, “to stand,” often translated as “office”). Yahweh won't wander anymore, and neither will His servants the Levites.
Their rest is a busy one. They stand at the hand of the priests to care for the courts and chambers of the temple, to prepare the tribute offerings of grain and bread, to offer praise and thanks and ascension offering, to guard the sanctuary and its sancta (vv. 28-32). Rest isn't inactivity for Yahweh, and it's not for the Levites either. To enter into rest is to enter into the service of the house of God, a place of perpetual Sabbath.
Most especially, the Levites enter rest in order to sing. Verse 30 states this explicitly, and verse 31 fills out the point. Levites were not permitted to approach the altar to make ascensions ascend; only priests could do that. Levites assisted with the slaughter and preparation of the animals for sacrifice, according to the number designated by Torah (cf. Numbers 28-29). But their song was a contribution to the offering of sacrifice. As the priests made animals ascend, the Levites sent up thanks and praise before Yahweh continually, morning and evening.
Levites entered rest. Their rest was service at the hand of the priests. Their rest was a service of thanks and praise. Entering rest, they entered the service of song.