WITH THE RESIGNATION of Frank Hodsoll, who will take a top-level job in the Office of Management and Budget, speculation runs high as to who will be the next chairman of the National Endowment for the Arts.

Four people who are being prominently mentioned as possible chairmen are: Schuyler Chapin, former dean of the Columbia University School of the Arts and a former general manager of the Metropolitan Opera; Barnabas McHenry, chairman of the Empire State Plaza Art Commission and co-vice chairman of the President's Committee on the Arts and Humanities. Milton Rhodes, president of the American Council for the Arts; and Lois Burke Shepard, director of the Institute for Museum Services, who spoke on the arts while campaigning for George Bush.All four have expressed interest in the job, and all have qualifications respected by such kingmakers as former NEA chairman Livingston Biddle and Kennedy Center founder Roger Stevens. Other possibilities being mentioned are Beverly Sills, Kitty Carlisle Hart, Lincoln Kirstein, Tony Randall, Stevens and artists Roy Lichtenstein, Robert Rauschenberg, and James Rosenquist.

A prerequisite is to get along with Rep. Sidney Yates, D.-Ill., of the House Appropriations Committee, who protected the NEA from Reagan budget cuts.

Meanwhile, Hodsoll named Hugh Southern, NEA deputy chairman, to fill in until the administration appoints a successor.

-HERBERT VON KARAJAN, the revered "conductor for life" of the Berlin Philharmonic Orchestra, has asked to be released from some provisions of his contract. At 80, Karajan has faced a number of painful health problems in recent years, and needs to reduce the number of concerts he conducts, citing back pain (he has had spinal surgery), tumor operations, a stroke, influenza, failing eyesight and hearing. "His life is a heroic exertion against illness and pain," said a Vienna music critic.

The move is sure to step up speculation over who will succeed Karajan in Berlin's top musical job. The list of contenders is said to include Claudio Abbado and James Levine.

-THE DETROIT SYMPHONY ORCHESTRA, facing an effort to block its funding on the basis of racism, hired its second black musician, bass player Richard Robinson. A part-timer with the orchestra, he will join it full time this fall.

Robinson's hiring came after two Detroit legislators threatened to block the symphony's annual allocation of $1.2 million in state funds. The officials charged the orchestra, based in a predominantly black city, was racist because it has employed only one black player for the past 12 years.

The orchestra has chosen its members through "blind" auditions, in which players perform behind a screen without revealing identities, but agreed to waive the selection process so that Robinson, 25, could be hired full time.

The symphony chairman pledged that it will not be another 12 years before more black musicians are hired. "We expect to continue making affirmative action progress while maintaining the highest standards," said Robert S. Miller.

The blind audition system is popular with symphony orchestras, since it removes the issue of color discrimination, and last summer the Detroit Symphony chose a black, cellist Owen Young, by this method. However, Young decided to return to Pittsburgh when invited.

Of the so-called Big Five orchestras, the New York Philharmonic and Boston each have one black player, the Chicago none, Philadelphia three and Cleveland two.

A dramatic influx of blacks into U.S. orchestras is not likely in the near future. Orchestra jobs are scarce, competition is fierce and black enrollment in the country's leading conservatories is minimal.

A 1987 survey of the nation's 10 major conservatories, conducted by the Peabody Institute in Baltimore, revealed that black students majoring in orchestral instruments ranged from zero to 13 at the 10 conservatories, for a total enrollment of just 56.

-DEATHS IN THE ARTS: Academy Award-winning Lionel Newman, 72, died in Hollywood. A 50-year veteran of 20th Century Fox studios, he composed, conducted or supervised the scores on more than 250 films.

Part of a prolific show business family, he followed his older brother Alfred to 20th Century Fox in the early 1940s, after composing and conducting for "Earl Carroll's Vanities," and working as a pianist for Mae West.

His brother Emile headed the music department at the Samuel Goldwyn Studio. Brother Marc was a musicians' agent, and a fifth brother, Robert, was a studio executive. His nephew is singer and songwriter Randy Newman.

Soprano Hilda Gueden, a favorite at the Met during the '50s and at the Vienna State Opera, where she was awarded the title of kammersaengerin, died in Vienna at age 71. In recent years she headed the Vienna State Opera Studio, an international apprentice program.

- Compiled by Dorothy Stowe