In 2022 a new rule allows you can apply for the Texas homestead exemption in the same year that you purchased your home. You can file your application for the exemption at any time.
Your application must be mailed by April 30th to be processed in time for your fall property tax bill. If you apply after April 30th, the exemption will be applied retroactively. This is applies up to one year after the tax delinquency date. If you file after this date, then the exemption will be applied in the following tax year.
You can apply for the over-65 or disabled person exemption at any time. The exemption is applied retroactively if you file within one year of turning 65 or becoming disabled.