If the transfer occurred in December of 2020 and you file and pay your taxes by April 15th you will not have to pay estimated tax and you should not be charged any interest or late payment for this transition. Taxes don’t have to be paid in full until April the following year.
The Tax Implications
When you convert a traditional IRA to a Roth, you will owe taxes on any money in the traditional IRA that would have been taxed when you withdrew it. That includes the tax-deductible contributions you made to the account as well as the tax-deferred earnings that have built up in the account over the years. That money will be taxed as income for the year you make the conversion.
Note: If you made the conversion within the same organization they may have withheld 20% and if so this would be reflected on your 1099-R.
If you file for an extension then you should include tax on your conversion with that extension. In either case be prepared for the additional tax liability.
RayW7's answer is incorrect and may cost you penalty and interest if followed. If by January 15, 2021 you do not meet either the safe harbor of having paid 100% of last year's tax liability (110% for those with higher AGI) or the safe harbor of having paid 90% of your 2020 tax liability, you must make a fourth quarter estimated tax payment. The deadline for making a fourth quarter estimated tax payment needed to avoid an under-withholding penalty is January 15, 2021.
The tax system is pay as you go, if you don’t pay estimated taxes, you can be assessed and under payment penalty even if you pay in full by April 15. The under payment penalty is about 1% per month which includes a penalty and interest. For a lump sum of income that you received in the fourth quarter of 20 20, the estimated payment is due by January 15, 2021. You can make a payment at www.irs.gov/payments. If you pay too much, you will get the excess back as part of your refund. Be sure to indicate on the estimated taxes paid page of TurboTax that you made the tax payment.