Verses 39-43 are no longer about the clan of Kohath, but about the clan of Gershom. For this reason it is helpful to begin a new paragraph here (so Good News Translation).

And his brother Asaph: The pronoun his refers to Heman (verse 33). In this context the Hebrew word translated brother actually means “relative” (Contemporary English Version) or, more broadly, “colleague” (Bible en français courant) or “helper” (New Century Version). New International Version translates his brother as “Heman’s associate,” while New Living Translation says “Heman’s first assistant.”

Who stood on his right hand: This clause is parallel with “on the left hand” in verse 44. In many languages it will be more natural to say “who stood by his right side.” For the first half of this verse Parole de Vie has “To the right of Heman, there was his colleague Asaph.”

Namely, Asaph the son of Berechiah …: The ancestors of Asaph are listed in verses 39-43, going back to Levi. As in verses 33-38, Good News Translation omits the repetition of son of in these verses, but makes it clear that each successive name refers to an earlier generation by saying that Asaph’s “family line went back to Levi.” In the Hebrew text the name Berechiah is written “Berechyahu” (so Nouvelle version Segond révisée, Traduction œcuménique de la Bible).

Quoted with permission from Omanson, Roger L. and Ellington, John E. A Handbook on 1-2 Chronicles, Volume 1. (UBS Helps for Translators). Miami: UBS, 2014. For this and other handbooks for translators see here .