Bede

There is, however, no discrepancy, for both were there, when David came to ask for bread, and received it: that is to say, Abimelech, the High Priest, and Abiathar his son; but Abimelech having been slain by Saul, Abiathar fled to David, and became the companion of all his exile afterwards. When he came to the throne, he himself also received the rank of High Priest, and the son became of much greater excellence than the father, and therefore was worthy to be mentioned as the High Priest, even during his fathers life-time.

Catena Aurea by Aquinas ↗