Tsarnaev has been charged with using a weapon of mass destruction during the April 15 marathon. Three people were killed and more than 260 injured when two bombs exploded near the finish line.
The suspect's lawyers could renew their motion to appoint another death penalty expert if he is indicted, the judge said.
Clarke's clients have included the Unabomber, Ted Kaczynski; Susan Smith, who drowned her two children; Atlanta Olympics bomber Eric Rudolph; and most recently Tucson, Ariz., shooter Jared Loughner. All received life sentences instead of the death penalty.
Clarke has rarely spoken publicly about her work and did not return a call seeking comment Monday. However, at a speech Friday at a legal conference in Los Angeles, she talked about how she had been "sucked into the black hole, the vortex" of death penalty cases 18 years ago when she represented Smith.
"I got a dose of understanding human behavior, and I learned what the death penalty does to us," she said. "I don't think it's a secret that I oppose the death penalty."
Bruck has directed Washington and Lee's death penalty defense clinic, the Virginia Capital Case Clearinghouse, since 2004.
In other developments in the Boston case:
• FBI agents visited the Rhode Island home of the in-laws of the suspect's brother, Tamerlan Tsarnaev, and carried away several bags. The brother was killed in a gun battle with police.
Katherine Russell, Tsarnaev's widow, has been staying at the North Kingstown home and did not speak to reporters as she left her attorneys' office in Providence later in the day. Attorney Amato DeLuca says she's doing everything she can to assist with the investigation.
• President Barack Obama and Russian President Vladimir Putin discussed terrorism coordination Monday in the wake of the Boston Marathon bombings. Obama expressed his "appreciation" for Russia's close cooperation after the attack.
The suspected bombers are Russian natives who immigrated to the Boston area. Russian authorities told U.S. officials before the bombings they had concerns about the family, but only revealed details of wiretapped conversations since the attack.