John Lightfoot on Luke 20:1

[The chief priests and the scribes with the elders.] So it is in Mark 11:27: but in Matthew 21:23, it is the chief priests and elders of the people. Now the question is, who these elders should be, as they are distinguished from the chief priests and the scribes. The Sanhedrim consisted chiefly of priests, Levites, and Israelites, although the original precept was for the priests and Levites only. "The command is, that the priests and Levites should be of the great council; as it is said, Thou shalt go unto the priests and Levites: but if such be not to be found, although they were all Israelites, behold, it is allowed."

None will imagine that there ever was a Sanhedrim wherein there were Israelites only, and no priests or Levites; nor, on the other hand, that there ever was a Sanhedrim wherein there were only priests and Levites, and no Israelites. The scribes, therefore, seem in this place to denote either the Levites, or else, together with the Levites, those inferior ranks of priests who were not the chief priests: and then the elders, may be the Israelites, or those elders of the laity that were not of the Levitical tribe. Such a one was Gamaliel the present president of the Sanhedrim, and Simeon his son, of the tribe of Judah.