The Texas Tribune media bias rating is Lean Left.

The Texas Tribune is a nonprofit news organization based in Austin, Texas. Founded in 2009 by venture capitalist John Thorton, it describes itself as the "only member-supported, digital-first, nonpartisan media organization that informs Texans — and engages with them — about public policy, politics, government and statewide issues." It claims to have the largest statehouse news bureau in the United States, where it covers a wide range of topics, from public and higher education to health care, immigration, criminal justice, energy, and the environment. It also hosts The Texas Tribune Festival, which attracts thousands of attendees each year to discuss Texas' biggest challenges.

Though the Tribune is billed as being non-partisan, its coverage often exhibits a slight liberal bias, particularly on immigration and political issues. It's in a national partnership with the Washington Post, which has an AllSides rating of Leans Left. While the Tribune relies on a mostly member-driven funding model, it also receives large corporate sponsorship and grants from organizations like the John S. and James L. Knight Foundation and the Bill and Melinda Gates Foundation.

Sources:
Wikipedia

TexasTribune.org