On developed single-family lots only monarch trees (very large trees of listed species, or trees Council designates) are protected, and removing one needs City Council authorization. Other trees on an existing home lot are not protected. Ask Forestry whether your tree is a monarch.
How to apply: Apply through the City of Round Rock permit portal (Forestry). Residential permits are processed in about 15 working days; monarch tree removal must be authorized by City Council.
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: roundrocktexas.gov/city-departments/parks-and-recreation/for · roundrocktexas.gov/wp-content/uploads/2015/01/treetechnicalm · library.municode.com/tx/round_rock/codes/code_of_ordinances?