New International Version
2 Kings 23:
4a
The king ordered Hilkiah the high priest, the priests next in rank and the doorkeepers to remove from the temple of the LORD all the articles made for Baal and Asherah and all the starry hosts.
second in rank,
הַמִּשְׁנֶה֮ (ham·miš·neh)
Article | Noun - masculine singular
Strong's 4932: A repetition, a duplicate, a double, a second
Pulpit:
and the priests of the second order. Not the "deputy-high priests," of whom there seems to have been only one at this period of the history (2 Kings 25:18); nor the "heads of the courses," who were not recognized as a distinct class of priests till much later; but merely the common priests, as distinguished from the high priest. (So Keil, Bahr, and others.)
According to Pulpit, there were only high priests and common priests:
priests of the second order = common priests
Barnes' opinion was similar:
The priests of the second order - This is a new expression; and probably refers to the ordinary priests, called here "priests of the second order," in contrast with the high priest
The same Hebrew word is used to describe musicians in 1 Chronicles 15:
16David told the leaders of the Levites to appoint their fellow Levites as musicians to make a joyful sound with musical instruments: lyres, harps and cymbals.
17 So the Levites appointed Heman son of Joel; from his relatives, Asaph son of Berekiah; and from their relatives the Merarites, Ethan son of Kushaiah; 18and with them their relatives next in rank: Zechariah, b Jaaziel, Shemiramoth, Jehiel, Unni, Eliab, Benaiah, Maaseiah, Mattithiah, Eliphelehu, Mikneiah, Obed-Edom and Jeiel, the gatekeepers.
Here too, there seemed to be just two classes. In both cases, we are not talking about a huge number of people.
What were the priests of the second-order?
The jury is still out on this one. Interestingly, the Bible never mentions priests of the 3rd-order :)