How did the extinction of Siats allow small tyrannosaur dinosaurs to evolve into larger carnivores such as the Tyrannosaurus rex?

Siats, or more specifically, Siats meekerorum, was a species of giant dinosaurs that predated Tyrannosaurus Rex (or T. rex). Siats lived on Earth around 98 million years ago and went extinct between 98 million to 80 million years ago. At that time, the T. rex was comparatively a smaller dinosaur and was not the top predator. It is believed that the Siats and the tyrannosaurs co-existed for a while, with the former being the apex predators. The extinction of Siats caused an absence of the top predator in the ecosystem and resulted in the evolution of the T. rex as the top predator.
The fossil of Siats meekerorum was discovered in Utah in 2008 and is part of the carcharodontosaurs, which represents a group of giant predators. The Siats were estimated to have weighed a few thousand pounds (even the juvenile one whose fossil was discovered weighed around 9000 pounds); they were more slender than the T. rex and had three digits.
Hope this helps.