Within 6 to 12 months before their test, but not earlier. One year of prep seems to be perfect for the SHSAT and other high school entrance exams. For the most part, the same is true for other tests such as the SATs.
Subject tests such as the Regents and the SAT Subject Tests usually require 3 to 9 months- depending on class performance.
Most timed standardized exams test students on similar skills. The skills developed for one test will carry over to your child’s prep for their next test. If your child recently prepped for a similar test, then they won’t need to study as much as they would otherwise. So, it depends.
You can always start early and slow down the prep as your child achieves their desired score. The earlier they begin, the more practice tests they can take. Taking more practice tests results in higher confidence and better scores.