John Gill Commentary 1 Chronicles 24

Now these are the divisions of the sons of Aaron Into the classes or courses following:

the sons of Aaron; Nadab and Abihu, Eleazar and Ithamar (1 Chronicles 6:3) , these were the immediate sons of Aaron; but the division or distribution of them into classes are of their posterity in the times of David, who descended from the two latter.

But Nadab and Abihu died before their father
While he was living, see (Leviticus 10:1Leviticus 10:2)

and had no children, therefore Eleazar and Ithamar executed the
priests' office :
otherwise, as Jarchi observes, had their brethren left children, they would have come into the office before them.

And David distributed them
The descendants of Eleazar and Ithamar into certain classes or courses:

both Zadok of the sons of Eleazar, and Ahimelech of the sons of
Ithamar ;
these were the two principal men of the respective families, the one was high priest, and the other "sagan" or deputy; or they both officiated as high priests alternately, until the one was removed in Solomon's time, and the other established alone. And now their brethren the priests, who were under each of these, are the persons David divided into classes:

according to their offices in their service :
to perform their office as priests in the service of the temple in their turns.

And there were more chief men found of the sons of Eleazar than
of the sons of Ithamar
Or heads of men, heads of their fathers' houses and families:

and thus were they divided; among the sons of Eleazar there were
sixteen chief men of the house of their fathers, and eight among the
sons of Ithamar, according to the house of their fathers ;
in all twenty four, and into so many classes or courses did David divide them; Jarchi says at first when the tabernacle was at Shiloh, there were but sixteen courses, eight from Eleazar, and eight from Ithamar, as is explained in the treatise of fasting ^F14 ; but when David saw that there were more heads of men, or chief men of Eleazar's, he divided the courses of Eleazar into two parts, and fixed sixteen courses; and the courses of Ithamar he established as at first, eight courses; left them as they were, which he thinks appears from (1 Chronicles 24:6).

but of the former number of courses, and when and by whom fixed, the Jews are divided ^F15 ; (See Gill on Luke 1:5). Perhaps there were none before David's time.

FOOTNOTES:

• F14: T. Bab. Taanith, fol. 27. 1.
• F15: T. Bab. Taanith, fol. 27. 1.

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.