You will need to amend your 2021 tax return to enter the 2021 Form 1099-G.
An amended return, Form 1040-X, can only be printed and mailed to the IRS if the original tax return was not e-filed. The IRS will take up to 16 weeks or longer to process an amended tax return.
Before starting to amend the tax return, wait for the tax refund to be received or the taxes due to be paid and processed by the IRS.
See this TurboTax support FAQ for amending a 2021 return - https://ttlc.intuit.com/community/tax-return/help/how-do-i-amend-my-2021-return/00/2544441