Jamieson, Fausset and Brown on 1 Chronicles 27:16

16. over the tribes of Israel: the ruler--This is a list of the hereditary chiefs or rulers of tribes at the time of David's numbering the people. Gad and Asher are not included; for what reason is unknown. The tribe of Levi had a prince (1Ch 27:17), as well as the other tribes; and although it was ecclesiastically subject to the high priest, yet in all civil matters it had a chief or head, possessed of the same authority and power as in the other tribes, only his jurisdiction did not extend to the priests.