The TurboTax online editions for tax year 2021 will not be available until sometime in early December.
The TurboTax desktop CD/Download editions for tax year 2021 are available now on this website - https://turbotax.intuit.com/personal-taxes/cd-download/
You can use the TurboTax calculator TaxCaster to get an estimate of the tax refund or taxes owed - https://turbotax.intuit.com/tax-tools/calculators/taxcaster/
Sometime in the next two weeks (i.e. early December) ..... Premier "Online" should be available. Just log into your account every few days and see if it's "up".
It will be somewhat buggy until mid-late January, so some things may not be calculating fully and correctly at the start. Don't even bother trying to go to your state file section until late January.
realize that when they become available they will not reflect all the law changes for 2021. e-filing likely will not open until mid-February. However, that does not mean the IRS/State have finalized all forms. some forms may be later and if your return contains them, you won't be able to e-file until they're finalized.
You will not be able to actually file a tax return until late January. Entering estimates now, rather than actual accurate data, will not allow you file any sooner and increases the chances of errors being made on your tax return.