Albert Barnes Commentary 1 Kings 2:27

"So Solomon thrust out Abiathar from being priest unto Jehovah, that he might fulfil the word of Jehovah, which he spake concerning the house of Eli in Shiloh." — 1 Kings 2:27 (ASV)

That he might fulfill the word of the LORD - We should not understand this to mean that fulfilling the old prophecy was Solomon’s motive, or even one of his motives. The reference is to the overruling providence of God, which brought about the fulfillment of the prophecy in this way. (Matthew 2:15; Matthew 27:35, and so on.) The deposition of Abiathar involved the rejection of the house of Ithamar (1 Chronicles 24:3), to which Eli belonged, and the reestablishment of the high priesthood in the line of Eleazar.