Gerard Schwarz had the kind of problem we would all like to have. His life's ambition was not a modest one, but he fulfilled it in his youth. So, naturally, he decided to have another life's ambition (also not modest), which is just about fulfilled in his mid-thirties.

"I was 13 years old--no, 12," he recalls, "when I decided I wanted to be a trumpet player--and not only a trumpet player but the first trumpet of the New York Philharmonic. Ten years later, there I was."

A few months after getting the Philharmonic job, Schwarz decided that what he really wanted to be was a conductor. For three years, he sat in the Philharmonic's trumpet section, watching such conductors as Leonard Bernstein, Pierre Boulez and Erich Leinsdorf, observing fine points of their technique and muttering to himself, "I can do that." Since leaving the Philharmonic in 1975, he has been proving that indeed he can. He will prove it again tonight at the Kennedy Center when he conducts a program of the Mostly Mozart Festival, for which he has been named to the newly created position of music adviser.

Seven years after leaving the Philharmonic, he still remembers the perennial anxiety that haunts all trumpet players: his lip. "You have to worry so much about that little part of your body, 1 1/2 inches square," says Schwarz. "I remember I would go outdoors and look at my house and say to myself, 'I own this house, I support my family because I make noise with this brass tube.' "

Not anymore; besides being the music director of two orchestras and two summer festivals, Schwarz is a busy guest conductor--busier than some free-lance conductors who do nothing else. He will make his debut with the National Symphony next month in two programs of its Beethoven festival and will be back in December to conduct Handel's "Messiah."

He has played the trumpet only once in the last two years. That was on Martin Feinstein's birthday last April; Schwarz called him long-distance and trumpeted "Happy Birthday to You" over the phone. It was a touching gesture for a friend who was recovering from a heart attack, and a tribute to the man who will give Schwarz the opportunity for his next musical breakthrough: conducting opera. Schwarz has conducted concert performances of operatic material before, but when he raises his baton for Mozart's "Abduction from the Seraglio" next season in the Terrace Theater, it will be his first time in an opera pit. Obviously, the Washington Opera has great expectations of him; it has scheduled 13 performances in the first season of this production.

This will have a special meaning because opera was what first gave Schwarz his trumpet fixation--specifically, Verdi's "Aida," which offers the trumpet nearly as much glory as the soprano and tenor.

Schwarz is the son of two doctors who moved to the United States from Austria, settled in Weehawken, N.J., and brought their love of music with them. They started him on the piano when he was 5 and began taking him to the opera when he was 7. And they had mixed feelings when he told them he wanted to be a trumpeter, but they sent him off to the music camp at Interlochen, Mich., during the summer of his 12th birthday, and that was when an interest became a tightly focused ambition. Part of the focus came from parental pressure.

"It went something like this," he recalls. "I played a lot of jazz; I loved it and listened to it all the time. My parents thought it was bad enough that their Jewish son was going to become a trumpet player, but to become a jazz trumpet player was absolutely out of the question. We had a big house with offices and a waiting room for my parents' patients. There was a big basement under the waiting room; my parents used it for entertaining and things like that, and I had a music room down there where I would practice. Whenever I got down there, I would try some jazz and my father would call me on the home phone from his office phone and tell me, 'No jazz.' So I'd get back to my e'tudes."

"They wanted me to play the piano," he recalls, "and they offered to help me with that--'But if you really want to play the trumpet,' they told me, 'you're on your own.' They weren't as tough as it may sound, but they worried about me and they wanted to be sure it wasn't a passing fancy. So I went out and worked to buy an instrument, to pay for lessons and sheet music and all those things. I shined shoes, and eventually I even started playing club dates when I was in high school to buy myself trumpets--you know, I had to have a C trumpet and a piccolo trumpet--lots of trumpets. And I learned about money and the work ethic and how hard it was, which is good to learn while you're young."

For Gerard Schwarz, the work ethic meant becoming a member of the American Brass Quintet and a conductor for the Eric Hawkins Dance Company when he was 17, and joining the American Symphony Orchestra when he was 18 and still a student at Juilliard. "I was traveling all over the world then with the brass quintet," he says. "It took me a long time to get my degree at Juilliard because I traveled so much. I would go to school usually for half a year and then travel." While he was still with the New York Philharmonic, after deciding that the trumpet was not his final destiny, he began moonlighting as a guest conductor for the Chamber Music Society of Lincoln Center, Speculum Musices, the Philharmonic Virtuosi, the Aspen Festival and other musical organizations.

After leaving the orchestra, he divided his time for awhile between free-lance trumpeting and conducting, but conducting jobs began to crowd out trumpet work, as he had hoped they would. In 1976, he was appointed music director of the Waterloo Music Festival in New Jersey (a job he still holds), and that experience led to his appointment as the first music director of the Y Chamber Symphony in Manhattan's 92nd St. Y, another job that he has kept. In 1978, he was a guest conductor with the Los Angeles Chamber Orchestra, and a few months later he was appointed to succeed Neville Marriner as its music director. Since then, he has conducted nearly 20 records with the Los Angeles orchestra, making it the most recorded orchestra in the United States last year.

In his earlier incarnation, of course, he already had recorded almost the entire repertoire for solo trumpet. "It's funny," he says. "When I made my last solo recording, I had the feeling that at last I was really getting somewhere with the trumpet. If I were still playing today, I would be better now than I was then. But that's not going to happen."

His parents are very happy.