Albert Barnes Commentary 1 Chronicles 29:22

"and did eat and drink before Jehovah on that day with great gladness. And they made Solomon the son of David king the second time, and anointed him unto Jehovah to be prince, and Zadok to be priest." — 1 Chronicles 29:22 (ASV)

King the second time - Solomon’s first appointment was at the time of Adonijah’s rebellion. As that appointment was hurried and relatively private, David now thought it best to formally invest Solomon with the sovereignty a second time, in the presence of all Israel.

For a similar reason, a second and public appointment of Zadok alone to the high priest’s office took place. Abiathar was not yet completely thrust out, but it is doubtful whether he was ever allowed to perform high-priestly functions after his rebellion (1 Kings 1:7; 1 Kings 2:27).