Jamieson, Fausset and Brown on 1 Chronicles 24:3

3. Zadok ... and Ahimelech of the sons of Ithamar--This statement, taken in connection with 1Ch 24:6, is not a little perplexing, since (2Sa 15:24, 35; 20:25) Abiathar is mentioned as the person conjoined in David's time with Zadok, in the collegiate exercise of the high priesthood. Some think that the words have been transposed, reading Abiathar, the son of Ahimelech. But there is no ground for regarding the text as faulty. The high priests of the line of Ithamar were the following: Ahiah or Ahimelech, his son Abiathar, his son Ahimelech. We frequently find the grandfather and grandson called by the same name (see list of high priests of the line of Eleazar, 1Ch 6:30-41). Hence the author of the Chronicles was acquainted with Ahimelech, son of Abiathar, who, for some reason, discharged the duties of high priest in David's reign, and during the lifetime of his father (for Abiathar was living in the time of Solomon, 1Ki 2:27) [Keil].