If you buy a home as your primary residence in 2018, you can file for a homestead exemption for that home for 2019 by occupying the home as your primary residence on January 1, 2019. You would want to have the utilities on and in your name and have some personal effects in the home if you have not completely moved in prior to January the 1st.
This exemption could save you between 15% to 20% on your tax bill. Remember that the taxes shown on HAR listings should be before any homestead exemptions. If the home you are buying is your primary residence, your actual tax bill will be less than reflected in HAR when you bought the home in most cases. Valuations can change each year as well as tax rates can change.