By Alexander Osipovich

The New York Stock Exchange is set to reopen its famed trading floor Tuesday, but it won't be going back to normal.

Only one-quarter of the NYSE's usual population of traders will be back when the floor resumes business after a two-month closure prompted by the coronavirus pandemic. Traders who return must wear masks, avoid taking public transportation and follow tough social-distancing rules, with newly erected Plexiglas barriers to help them stay apart.

A visitor ban means splashy bell-ringings and celebrations to mark initial public offerings won't be happening anytime soon. Media organizations that broadcast from the floor, like CNBC and Cheddar, aren't coming back yet either.

To return to their jobs, floor traders must sign a liability waiver that prevents them from suing the NYSE if they get infected at the exchange. They must acknowledge that returning to the floor could result in them "contracting Covid-19, respiratory failure, death, and transmitting Covid-19 to family or household members and others who may also suffer these effects," according to the waiver, a copy of which was seen by The Wall Street Journal.

The waiver has fueled tensions between the NYSE, owned by Intercontinental Exchange Inc., and some Wall Street firms with representatives on the floor.

Floor traders aren't exchange employees, but instead work for various banks, brokerages and trading firms. The NYSE has asked such firms to sign an agreement under which they would compensate the exchange for certain lawsuits arising from a Covid-19 outbreak, people familiar with the matter said. Some firms have balked at the agreement, including Morgan Stanley, which isn't planning to send its brokers back to the floor, the people said. A NYSE spokeswoman declined to comment on the dispute.

Still, many traders are expected to sign the waivers and go back, particularly floor brokers who work for smaller firms and have been strapped for cash during the closure.

Many floor brokerages -- which execute trades at the NYSE on behalf of clients like banks and asset managers -- have fewer than 20 employees, and their revenue dried up during the closure. Some got loans under the Paycheck Protection Program to cover lost income.

"I feel confident that the health and safety of the floor community is the NYSE's No. 1 priority," said Jonathan Corpina, senior managing partner at Meridian Equity Partners, a floor brokerage. "I have no doubts about going back to the floor."

Meridian plans to have six brokers, including Mr. Corpina, back on the floor this week. Before the closure, the firm had 15 brokers on the floor on a typical day. But now, most of Meridian's seats must stay empty to let brokers maintain a safe distance from one another.

The NYSE has one of the world's last stock-exchange trading floors, though its population has been decimated over the past 20 years as markets have gone electronic. NYSE officials say the floor remains useful because traders there can apply "human judgment" to transactions, especially large, complex ones like IPOs and the 4 p.m. auctions that determine end-of-day stock prices.

The floor is also an important part of the NYSE's brand, helping the exchange win listings from companies whose executives ring the opening bell and hold events at its historic building in lower Manhattan.

As the coronavirus pandemic gained force in March, the NYSE initially resisted closing its floor, while other U.S. exchanges closed theirs to curtail the spread of the virus. NYSE officials reversed course after a floor trader and an exchange employee tested positive for Covid-19.

Now, the NYSE is moving cautiously to limit the risk of a new outbreak. It devised its reopening plan with assistance from outside advisers including Scott Gottlieb, a former commissioner of the Food and Drug Administration under President Trump.

Floor traders must submit to temperature checks on entering the building, with blue markings on the sidewalk to ensure they stand 6 feet apart while waiting in line. Inside, they must avoid shaking hands or other physical contact. Eating on the floor is banned, to ensure masks stay on at all times, though traders can still have lunch at designated spots in the NYSE's cafeteria.

The floor will also be a quieter place with the designated market makers continuing to work remotely. Normally, such traders stand at posts in the middle of the floor and oversee trading in NYSE-listed stocks, and floor brokers can come up to them and shout out orders to buy or sell stocks. With the DMMs absent, that practice will be halted.

The NYSE will deep-clean its building daily after markets close, and a team of workers will clean frequently touched surfaces like door handles throughout the day. But even such precautions may not be enough to stop the virus, NYSE President Stacey Cunningham warned in a May 14 opinion piece in the Journal.

"For the NYSE and the nation as a whole, it's important to approach reopening with realistic expectations," she wrote. "While our plan is designed to reduce risk, it cannot eliminate it."

--Corrie Driebusch contributed to this article.

Write to Alexander Osipovich at alexander.osipovich@dowjones.com