Do I need a software update to use turbotax next year?

We cannot see your tax return or your operating system.   Each year has its own software so for your 2021 tax return you will need to use 2021 software.   If you are talking about the CD/download, you cannot update it to 2021---you have to buy the 2021 software.

Each tax year is a separate TurboTax program that has to purchased for each tax year.