For homes bought and sold in the same county sellers over 55 can transfer their current low tax base to a newly purchased home.
Proposition 60 was approved by California voters in 1986. As in any and all situations regarding your taxes you should always consult with your tax person (tax expert).
To qualify for Proposition 60 the home must be the principal residence and one of the property owners needs to be at least 55 years old on the day the house is sold. And, all Proposition 60 transactions must be completed within 2 years of the date of the sales.
(Photo of sailboats and Santa Barbara Harbor in the background from Instagram)