A charter amendment can be proposed by City Council under Texas Local Government Code 9.004: The City Council can propose Charter amendments on its own motion. Charter amendments can also be proposed by a petition: A citizen petition – signed by at least 5% of the number of qualified voters in the City or 20,000 – whichever is smaller.
Any changes to the city charter must be approved by a majority of qualified voters of the city at an election. Local Government Code §9.005. The charter cannot “be altered, amended or repealed oftener than every two years.” Tex. Const. Art. XI §5.
The city must follow certain procedures and steps outlined in the Texas Election Code and Local Government Code to order an election for a charter amendment.