The Klingon High Council was the ruling council of the Klingon Empire.
B'vat had advised the High Council not to allow Kardok's house to be reinstated nor his crimes nullified, due both to his father's and his own past deeds. Despite B'vat's objections, Kardok was not only permitted to return to the homeworld, but he was given command of a ship as well.
This may have been due in part to the High Council's growing distrust of B'vat, whose unorthodox battle tactics were deemed "radical." Some on the High Council even saw peace as a more viable option than B'vat's plans for the war.