The income levels in the previous comment are incorrect. Maybe he was thinking of a different program.
From the apply for STAR website:

Are you eligible for STAR?
If you own your home, it’s your primary residence, and
your income is $500,000 or less, you’re eligible for the
Basic STAR credit.

In addition, if you’re 65 or older with an income of $107,300 orless, you may be eligible forthe EnhancedSTAR credit.
In your first year at your new home, you may receive the prior owner’s STAR exemption. In future years, as
long as you’re eligible, you’ll receive a STAR credit payment. You don’t need to register again.