Trees 19" diameter and larger are Protected (any species) and need a permit to remove or to prune more than 25% of the canopy. Heritage trees (24"+ of listed species) need a variance; heritage variances for trees 30"+ go through a public process. The ordinance applies in Full and Limited Purpose areas, not the ETJ.
How to apply: Apply with the City Arborist (Development Services) for a residential tree permit.
Texas law: cities cannot charge a tree mitigation fee for a tree under 10" at an existing one- or two-family home you live in (Local Gov't Code §212.905, HB 7, 2017). Since 2023, landowners can petition to leave a city's ETJ (SB 2038), so ETJ lines change; we read the live City of Austin jurisdiction map.
Official sources: austintexas.gov/development-services/city-arborist · austintexas.gov/page/trees-residential-property