You can just file a federal extension in TurboTax. To do so, click on Search and type "Extension" in to the window. Next click on "Jump to Extension" to file an extension.
You can pay and file the New Jersey extension directly from the New Jersey Department of the Treasury website by going to: Individual Income Tax Payment and Filing - New Jersey
Tax Deadline Change and Information on Extension Requests
If you need more time to prepare your tax return, beyond the extended due date of May 17, you may apply for an extension of time to file. Be aware that:
If You Are Filing a Federal Extension
Provide us with a copy of your federal extension application (or confirmation number from the IRS) when you file your New Jersey tax return.
Civil union partners filing a joint return must either provide copies of the federal extension application (or confirmation number), or they must file Form NJ-630.
If You Are Not Filing a Federal Extension
File Form NJ-630 to request an extension with New Jersey no later than May 17, 2021. You may file the form:
You Must Pay At Least 80% of Your Tax Liability
In order for New Jersey to accept your extension, you must:
If you do not have at least 80% of your taxes paid by May 17, 2021, we will deny your extension and charge you a late filing penalty.