John Gill Commentary 1 Chronicles 24:5

"Thus were they divided by lot, one sort with another; for there were princes of the sanctuary, and princes of God, both of the sons of Eleazar, and of the sons of Ithamar." — 1 Chronicles 24:5 (ASV)

Thus were they divided by lot, one sort with another
Which course should serve first, and which next, and so on; and who should be the chief to each course; which course was to serve a week, and then go out; and this method was taken to prevent envy, strife, and contention about precedence:

for the governors of the sanctuary ;
or of the holy things, or who presided in things ecclesiastical:

and governors of the house of God :
or rather "governors of God", appointed by him judges in civil things:

were of the sons of Eleazar, and of the sons of Ithamar :
there were, of both families, some employed both in sacred and civil things, and who presided in each.