Pulled from (High) Priesthood

  1. Eleazar, son of Aaron
  2. Phinehas
  3. Abishua
  4. Bukki
  5. Uzzi

From Ithamar's line (right in time for the Monarchy)

  1. Eli  , grandson of Aaron through Ithamar
  2. [skipped?]
  3. Ahitub, grandson of Eli
  4. Ahijah
  5. Ahimelech (possibly brother of Ahijah in which case, the son of Ahitub)
  6. Abiathar, son of Ahimelech