If the Form 1099-G was for tax year 2021 then you will have to amend the 2021 tax return to add the form. It cannot be added to any other tax return.
See this TurboTax support FAQ for amending a 2021 tax return originally completed and filed using TurboTax - https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-return/amend-2021-return/L1gEU4G3X_U...
