Warning: SPOILERS for Godzilla Vs. Kong.
Godzilla let Kong live in Godzilla Vs. Kong as the MonsterVerse mash-up film found a clever way to let both kaiju shine and even form an alliance to battle and defeat Mechagodzilla. Although Godzilla's goal in Godzilla Vs. Kong was initially to kill the massive primate in order to reassert his status as the King of the Monsters, the circumstances of their clashes as well as how Kong helped him destroy Mechagodzilla changed Godzilla's mind. Their truce left the Earth with two alpha Titans, one for the surface world and one to rule the Hollow Earth.
Godzilla Vs. Kong takes place three years after the events of Godzilla: King of the Monsters. In that film, King Ghidorah was awakened from his Millennia-long Antarctic slumber, which then set off the rising of over a dozen other Titans around the world. The monsters were summoned by Ghidorah, who set out to become their ruler and the destroyer of the world. With the help of Monarch, Godzilla ultimately killed Ghidorah and established himself as the King of the Monsters. But the only great Titan who didn't submit was Kong, the ruler of Skull Island. In fact, to keep Godzilla from attacking Kong, Monarch built a containment dome over Skull Island. As seen in Kong: Skull Island, ever since Monarch first encountered Kong in 1973, the monster-fighting agency has regarded Kong as a friendly Titan who deserves protection.
In Godzilla Vs. Kong, Monarch broke their own containment of Skull Island when they joined with Apex Cybernetics to transport Kong to Antarctica. Their plan was to use Kong as a guide to lead them into the Hollow Earth, where Apex hoped to harness the ancient energy source that powers all of the Titans. However, Monarch knew that Kong was vulnerable to attack from Godzilla during their sea voyage to the South Pole. Sure enough, Godzilla sensed Kong's presence in the ocean and the radioactive lizard went after his main rival. Kong was at a severe disadvantage against Godzilla in the deep sea and the ape was nearly drowned. Kong's human guardians finally saved his life by tricking Godzilla into thinking Kong submitted. Godzilla left Kong alive and departed, satisfied with his victory, while Kong and the Monarch/Apex alliance continued to Antarctica.
Kong and Godzilla had a rematch when the lizard sensed the ape had found his ancestors' ancient throne room in the Hollow Earth. When Kong used a battle-ax made from a Godzilla's dorsal fin to activate the Hollow Earth's power source, Godzilla used his Atomic Fire Breath to burn a tunnel into the center of the Earth. Kong climbed up and found Godzilla in Hong Kong, where they had their rematch. With his ax, which could absorb Godzilla's atomic breath, Kong pummeled the lizard and scored a brief victory. But Godzilla came back and overwhelmed Kong, ultimately triumphing over the ape. While the two Titans roared at each other as Godzilla stomped on the ape's heart, Kong dropping his ax was what signaled his tapping out to Godzilla. The lizard left Kong to die via heart-stoppage when he was satisfied that the ax made from his ancestor's fin was no longer a threat.
The emergence of Mechagodzilla, which was actually under the control of the resurgent Ghidorah, changed everything between Godzilla and Kong. Godzilla was completely overpowered by his robotic doppelganger. Kong's human allies then used the Hollow Earth energy as a defibrillator to jumpstart Kong's heart. With the mighty ape back in the fight, Kong and Godzilla combined their powers to completely destroy Mechagodzilla - and end the threat of King Ghidorah once and for all.
It was the fact that Kong came to his rescue that really seemed to change Godzilla's mind about the primate, which is why he decided not to kill Kong. Instead, Godzilla acknowledged Kong as an equal and he returned to the sea. While it's impossible to know for sure what's in the hearts and minds of giant monsters, Kong apparently earned Godzilla's respect so the lizard left him alone. Luckily, the world is big enough for two alpha Titans. Godzilla Vs. Kong's fitting ending saw Godzilla resume his dominance over the surface world while Kong returned to the Hollow Earth and took his rightful place as its ruler.