No quarterly payments, but a deadline that matters
Utah doesn't require quarterly estimated income tax payments. You can prepay at any time online or by mailing Form TC-546.
You get an automatic six-month extension to file, but not to pay. To avoid a penalty, you need to have paid the lesser of 90% of this year's tax or 100% of last year's by the original due date. Otherwise, the penalty is 2% of the unpaid tax for each month of the extension.