Whether you have lost your health insurance or simply want a better deal on coverage, here is some good news: Under a Covid-19 stimulus bill Congress passed in March, many people who buy Affordable Care Act plans can qualify for premiums that are cheaper—or even free.

It is important to act fast because the window for most people to enroll for 2021 closes Aug. 15, said Karen Pollitz, a senior fellow specializing in private health insurance at the nonprofit Kaiser Family Foundation.

Here are details on who is eligible for premium assistance, how the assistance works and what to consider before switching policies.

What has changed?

The stimulus bill increases premium subsidies in 2021 and 2022 in plans sold by the government-run marketplaces the ACA created. Some people, including those who received unemployment insurance this year, can get subsidies that may entirely eliminate their premiums.

For this year and next, the law also does away with a previous income limit on premium assistance, paving the way for some people with incomes as high as $149,000 to benefit.

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The higher subsidies may deliver significant savings to older people, especially those who previously didn’t qualify for premium assistance. Under the ACA, insurers can charge older people up to three times the premiums participants in their early 20s pay, said Joseph Newhouse, an economist at Harvard University.

Because of the enhanced subsidies, people who bought non-ACA compliant policies on the individual market should look on the ACA marketplace “to see if they can find more affordable coverage,” Ms. Pollitz said.

Who is eligible for ACA coverage?

Citizens and legal residents of the U.S.

What kind of coverage can I get?

Most ACA-compliant plans come in four categories: platinum, gold, silver, and bronze. Respectively, they are designed to cover 90%, 80%, 70% or 60% of medical expenses for enrollees.

If you choose a bronze plan, you’ll generally pay lower premiums. But your annual deductible may be as high as $8,000. In contrast, annual deductibles average nearly $5,000 for silver plans, about $1,500 for gold plans, and below $1,000 for platinum plans, according to Ms. Pollitz.

Who isn’t eligible for subsidies?

If you’re entitled to Medicaid or Medicare, you can’t get premium subsidies. The same is generally true if you’re eligible for an employer-sponsored health plan.

Before the new law, subsidies were generally off-limits to individuals with incomes above $51,040 and families of four above $104,800.

Now, there is no income limit. But because of the way the subsidies work, individuals with incomes above an amount that varies by factors including age—about $50,000 for a 21-year-old and $135,000 for a 60-year-old—are unlikely to receive a benefit by claiming them.

How do the subsidies work?

Subsidies cap your premium payments at a percentage of household income. The lower your income, the smaller the percentage you’ll pay.

Thanks to the new law, subsidies are more generous than before.

Last year, an individual with income below $19,140 generally paid 4.14% of that amount for premiums. Now, the federal government picks up the entire cost.

Individuals earning up to $51,040 now pay 8.5% of income, down from nearly 10%. Those who earn more also can cap their premium contributions at 8.5% of income.

That can mean big savings for some. Consider a 64-year-old woman with a $52,000 salary. In 2020, she would have paid the full cost of her premiums, typically about $12,000 a year, said Ms. Pollitz. Now, she will owe 8.5% of her income, or about $4420.

A person that age “would have to earn well into the six figures” before it costs less to pay the full premium than it would cost to pay 8.5% of income, Ms. Pollitz said.

There is also a special deal for the unemployed—but only this year.

Anyone who received unemployment insurance “at any point this year, even for a week, is automatically qualified” to pay nothing for premiums on some plans, Ms. Pollitz said. To qualify, you must not be eligible for job-based health insurance. And if you’re married, you must file a joint tax return.

Are subsidies more generous for higher-cost plans?

No. Premium subsidies are calculated on the cost of a so-called benchmark plan, which is the second cheapest silver plan on the market where you live.

Someone with income below $19,140 qualifies for free premiums on a benchmark silver plan. If the person wants a gold or platinum plan instead, he or she must pay the difference between the premium and the subsidy.

Where can I sign up?

More than a dozen states, including California and New York, have their own marketplaces. (Some, including New Jersey and California, have extended the sign-up deadline beyond Aug. 15.) Others use Healthcare.gov, run by the federal government.

If you sign up by Aug. 15, your coverage typically begins Sept. 1.

Can people already in ACA-compliant plans get the higher subsidies?

Yes. For current enrollees, the higher subsidies are retroactive to Jan. 1.

To make sure your premiums for the remainder of the year reflect any extra subsidies you are entitled to, sign into your marketplace account and update your application.

You can claim any premium subsidies you missed out on when you file your taxes in April, Ms. Pollitz said.

How long will the higher subsidies last?

They are scheduled to remain in effect through the end of 2022. Democrats in Congress are pushing to make them permanent. “We should know sometime this fall if Congress is going to act,” said Ms. Pollitz.

What if I miss the Aug. 15 sign-up deadline?

Unless you live in a handful of states that are allowing enrollment after Aug. 15 or experience a so-called qualifying event such as a divorce or loss of health coverage, you won’t be able to get ACA-compliant coverage for 2021.

During the program’s annual open enrollment, which starts on Nov. 1 and typically ends Dec. 15, you can elect coverage with the higher subsidies for 2022.

I have free premiums under Cobra that will end soon. Should I switch to an ACA-compliant plan now?

The stimulus legislation gave many workers who have been laid off since the pandemic began the option to resume employer-based health insurance under Cobra without paying premiums from April 1 to Sept. 30. That federal law requires companies with 20 or more employees to allow departing workers to stay enrolled in the health plan, typically for up to 18 months.

If you have free premiums under Cobra, you can switch to an ACA-compliant plan whenever your free premiums end, even after Aug. 15, said Ms. Pollitz.

Alternatively, you can elect to remain on Cobra. Despite subsidizing workers’ premiums during employment, many companies can—and often do—require those on Cobra to pay the entire cost of their premiums plus a 2% annual administrative fee, said Ms. Pollitz.

How should I compare my options?

When comparing health insurance plans, consider premiums, deductibles and copayments.

Look also at provider networks and drug coverage, said Prof. Newhouse, who said employer-based health plans often provide more generous coverage than ACA plans.

If you already have met your Cobra plan’s deductible, you might want to remain on that plan for the rest of the year, even if it means paying the full cost of Cobra premiums for the final months of 2021, said Ms. Pollitz. That is in part because if you switch to an ACA-compliant plan midyear, you’ll be responsible for the deductible on the new plan.

Write to Anne Tergesen at anne.tergesen@wsj.com