Appraisal Cap
The 10% Appraisal Cap Protects Harris County Homeowners From Runaway Values
Once you have a homestead exemption in Harris County, your taxable property value cannot rise more than 10% per year — no matter how fast the market moves.
The appraisal cap kicks in starting the second year your homestead exemption is in place. Even if HCAD believes your home is worth 20% or 30% more than last year, your taxable value can only increase by 10% plus the value of new improvements.
The cap does not apply in your first year of ownership — HCAD resets the value when you buy. It also resets when you add major improvements. The cap applies only to the property's appraised value for tax purposes, not to the market value HCAD tracks separately. File your homestead exemption as soon as you buy your home — the cap does not start until the exemption is in place.
Source to confirm: HCAD – Property Tax Exemptions for Homeowners