Spoiler warning: Plot and/or ending details follow.
After the death of his son at the Battle of Pahvo, Kol-Sha assumed the leadership of the House of Kor and succeeded his son as the House's representative on the High Council. As a man of the "old ways" he opposed Chancellor L'Rell's attempts to unify the Klingon Empire unless it was on his terms, and viewed L'Rell's torchbearer Ash Tyler with deep suspicion.
Kol-Sha soon learned that Voq and L'Rell had conceived a son before Voq underwent the choH'a' surgery to transform him into Tyler. Kol-Sha had L'Rell's uncle Ujilli killed and kidnapped the child. Kol-Sha told L'Rell unless she handed power over to him he would kill the child.
After defeating several of Kol-Sha's people, L'Rell and Tyler were stunned by Kol-Sha, who used L'Rell's thumbprint to sign the abdication document. Before he could kill either Tyler or L'Rell Section 31 agent Philippa Georgiou burst in to the room and killed Kol-Sha's people. She then incapacitated Kol-Sha and released Tyler and L'Rell from their paralysis.
L'Rell proceeded to disembowel Kol-Sha. Georgiou convinced her that the truth would further fracture the Empire. L'Rell sent Tyler and their son away after faking their deaths. She then told the High Council that Tyler had murdered her son and was about to kill her, but Kol-Sha had intervened and died saving L'Rell's life. (DSC episode: "Point of Light")