Unless you received an advance payment for insurance bought through one of the exchanges, you don't need to do anything. If you did receive an advance payment and didn't complete Form 8962, you will need to file an amended return.
According to the IRS:
Beginning in tax year 2019, Form 1040 will not have the “full-year health care coverage or exempt” box and Form 8965, Health Coverage Exemptions, will no longer be used. You need not make a shared responsibility payment or file Form 8965, Health Coverage Exemptions, with your tax return if you don’t have minimum essential coverage for part or all of 2019.
You may receive multiple information forms that you can use to complete your tax return and will keep with your tax records.
The information forms are:
If you or your family received advance payments of the premium tax credit through the Health Insurance Marketplace, you must complete Form 8962, Premium Tax Credit with your return. You will receive Form 1095-A, Health Insurance Marketplace Statement, which provides you with information about your health care coverage. You should wait to file your income tax return until you receive that form. Use the information from Form 1095-A to complete Form 8962 to reconcile advance payments of the premium tax credit or – if you are eligible – to claim the premium tax credit on your tax return. Filing your return without reconciling your advance payments will delay your refund and may affect future advance credit payments.
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