1 Chronicles 23:7, 9, “The sons of Gershon were Ladan and Shimei…The sons of Shimei: Shelomoth, Haziel, and Haran, three. These were the heads of the fathers houses of Ladan.” ESV
“The man Shimei mentioned in this verse was the head of a subdivision in the family of Laadan, which was a smaller part of the Gershon clan. The man named Shimei mentioned in verses 7 and 10 was the son of Gershon (Ex. 16:17; Num. 3:18) and the founder of a division of the Gershon family.” ESV Hebrew-Greek Key Word Study Bible
This is not the Shimei who cursed David as he was fleeing from Absolom, see 2 Samuel 16:5-8.
1 Chronicles 26:1, “As for the divisions of the gatekeepers: of the Korahites, Meshelemiah, the son of Kore of the sons of Asaph.” ESV
“The man named Asaph mentioned here should not be confused with the psalmist, who had the same name and was a member of the clans of Gershon. The Korahites, who guarded the temple gates, belonged to the clan of Kohath.” ESV Hebrew-Greek Key Word Study Bible