The National Gallery of Art, which once disdained acquiring the work of living artists, will soon redouble its commitment to 20th-century painting. As one sign of that commitment, the museum has decided to appoint a second curator of 20th-century art. Though the position has not been filled, a likely candidate has emerged.

He is Jack Cowart, 38, the St. Louis art historian who organized the enormously successful show of Matisse's paper cutouts that opened at the gallery in 1977. His interests seem to be considerably more eclectic than those of E.A. Carmean, the gallery's other curator of 20th-century art.

While serving as curator of 19th- and 20th-century art at the St. Louis Art Museum, Cowart showed the austere grids of Agnes Martin, the edgy, streetwise visions of Chicago's Roger Brown, recent paintings by Willem de Kooning, and Cindy Sherman's photographs. Cowart also arranged "Roy Lichtenstein: 1970-1980," a traveling exhibit that just closed in Japan. His most recent touring show, a survey of new German expressionist painting, will be seen in Washington next summer at the Corcoran Gallery of Art. Cowart yesterday acknowledged that he has applied for the National Gallery's new job.

The decision to name a second curator of 20th-century art is part of what director J. Carter Brown calls "a long-range plan to beef up the scholarly end" of the gallery's endeavors.

When Brown assumed his post, the gallery was far better known for the art in its collections than for the scholarly accomplishments of its curators. In recent years, much institutional energy has gone toward expansion of the museum's physical plant--the construction of the East Building and the opening of more than 40 exhibition galleries on the ground floor of the West Building. With that construction completed, the gallery is busily expanding and improving its curatorial staff.

"We're getting a new team in place," says Brown. "It's really a new phase in the gallery's history."

A number of significant staff appointments have been made in recent months. They include:

* The hiring of S.J. Freedberg as chief curator. Freedberg, 68, a specialist in Renaissance and Baroque painting, comes to the museum after 30 years of teaching at Harvard University. Directors Philippe De Montebello of the Metropolitan Museum of Art, Everett Fahy of the Frick Collection, Earl A. Powell III of the Los Angeles County Museum of Art, and Brown are former Freedberg students. When he takes his post next week, he will be the best-known art historian in the gallery's employ.

* The promotions of John Wilmerding to deputy director and Andrew Robison to senior curator. Wilmerding, formerly the museum's curator of American art, was responsible for the Luminist and J.F. Peto exhibitions, two much-admired shows. Robison, despite his new title, will continue to supervise the gallery's department of prints and drawings. Their appointments, and that of Freedberg, confirm Wilmerding's remark that "Carter Brown wants senior scholars, rather than art bureaucrats, to run this institution."

* The hiring of Nicolai Cikovsky Jr., 50, as Wilmerding's replacement as curator of American art. Like Wilmerding and Brown, he was trained at Harvard; he received his PhD in 1965. A specialist in the art of George Inness and Winslow Homer, he was chairman of the art departments at the University of New Mexico, Albuquerque, and Pomona College in California. He also directed the art galleries at Pomona and Vassar College. Cikovsky's wife, historian Sarah Greenough, co-organized the gallery's recent Alfred Stieglitz exhibition; his father, who once taught at the Corcoran, is a painter whose murals decorate the Silver Spring post office and the Interior Department Building.

Cikovsky, who will join the staff Oct. 1, spent last year as a fellow at the gallery's Center for Advanced Study in the Visual Arts. The presence of that institution, run by Henry Millen, and the quality of its scholars may well have helped to strengthen Brown's determination to improve the scholarly credentials of his senior curatorial staff.

* The hiring of Susannah J. Fabing, another Harvard graduate, to fill a newly created post, chief of curatorial records. Fabing, who served as curator of ancient art, assistant director (1971-1979) and deputy director (1979-1983) of Harvard's Fogg Art Museum, has been given two assignments: She will make the gallery's archives and curatorial records accessible by computer; she also will supervise the publication of detailed catalogues of the gallery's collections.

* The promotion of Ross Merrill to the post of chief of conservation. Freedberg has promised to "encourage in every way an intimate collaboration between conservators and curators. I hope the curators will haunt the laboratories." Merrill, 40, a Texas-born painter, trained at Oberlin and worked at the Cleveland Museum of Art before joining the gallery staff in 1981. He replaces Victor C.B. Covey, who, freed from administrative responsibilities, is now the gallery's chief conservator emeritus and senior conservator for special assignments.