In Chief of War Season 1, Episode 4 titled, “City of Flowers Part II”, the political and spiritual race reaches to its peak when Keōua dramatically knocks out one of his own teeth. This is portrayed as a ritualistic gesture to symbolise the end of his mourning period and to mark his transition from grief into open hostility and warfare. He declares war on Kamehameha's faction, signalling that he doesn't hesitate to fight for what he believes is right.
Keōua gets to know that his deceased father has made not him but his brother Kamehameha the spiritual heir of the god of war, and he sees him as a bypass of his birthright. Therefore, by striking his tooth out, he showcases his strength and how tough a man he is. He further declares war by highlighting his broken tooth with his willingness to sacrifice for the sovereignty.
Here is what Keoua was trying to prove by breaking his own tooth in the Chief of War?

Keōua becomes furious when he discovers that his deceased father and the King have passed on the control of the military not to him, who is his legitimate child, but to his cousin brother Kamehameha. This makes him feel robbed of his birthright. He lashes out and calls Kamehameha a bastard son, and is determined to settle the issue in combat. When Kamehameha refuses, Keōua declares that Kamehameha may pray to the god of war for mercy,
“Then pray to the God of War for mercy. Because war has never been Kamehameha’s. But it has always been mine.”
This is when Keōua begins to punch his face hard, repeatedly, until his mouth starts to bleed and he takes a tooth out. He raises it before the others as a symbolic act of sacrifice.

Te Ao o Hinepehinga Curtis, who plays the role of Keōua in Chief of War, explained in his TV Insider interview that this wasn’t mindless savagery on the character's part, as in Hawaiian tradition, both blood and bone are sacred.
“As a higher chief of the highest born lineage, his blood is sacred. The other thing that is sacred is his bone. A sacrifice of any real value is your blood and your bones…to knock out a couple of teeth, it’s an accessible way of reaching your blood and bone to show the seriousness of intent. It seems quite savage, but there’s a psychological play here. [Kamehameha] doesn’t take the challenge. He doesn’t take him up on the fight. And so they must go to war.”
Therefore, Keōua breaking his tooth in the Chief of War signifies that he has shed his weakness and sorrow and is ready to sacrifice, suffer, and fight for his claim. The gesture seals his transition from a grieving son into a defiant challenger of Kamehameha’s rise, setting the stage for open conflict between the brothers.
The scene also works well emotionally as the character is going through turmoil in Chief of War, torn apart between his father's shocking decision, his mourning and grief and what he believes is right. The act is symbolic but also fits well to portray a state in which Keōua is, also highlighting his character, which signifies strength, courage, and a determination to win back the belief of his people.