As one of the "old guard", Kol-Sha adamantly opposed L'Rell's ascension to High Chancellor at the conclusion of the Federation-Klingon War in 2257. He constantly sought to undermine her rule, and demeaned her Torchbearer Ash Tyler as a Human "pet".
To spy on L'Rell's plans, Kol-Sha mixed sensor implants into the face paint that was the hallmark of his House, which he then wore in defiance of L'Rell's call for unity. As expected, Tyler challenged him and attempted to remove the paint, smearing the implants onto his hands. Through them Kol-Sha learned of a secret child L'Rell had conceived with Voq.
Kol-Sha abducted the infant, killing Ujilli in the process, and demanded that L'Rell give him control of the Klingon Empire in exchange for her son's safe return. L'Rell and Tyler chose instead to fight Kol-Sha's men, but Kol-Sha paralyzed them both with an energy weapon and compelled L'Rell's signing of the handover document.
Before Kol-Sha could assume leadership, he was ambushed and disabled by Philippa Georgiou. L'Rell promptly disemboweled Kol-Sha with her tajtIq. Realizing that the truth would fracture the Empire further, she manipulated the official record to claim that Kol-Sha had in fact died defending her from Tyler. (DIS: "Point of Light")