Conductor Christoph Eschenbach will not continue as music director of the National Symphony Orchestra after the 2016-17 season. (Scott Suchman/Kennedy Center)

When Deborah Rutter took over as the Kennedy Center’s president in September, music lovers wondered what would happen with the National Symphony Orchestra — one of the most highly paid ensembles in the country, but a chronically underperforming organization.

Now, there will be a chance to find out. The orchestra announced Wednesday that Christoph Eschenbach, the internationally acclaimed — but uneven — conductor who has served as its music director since 2010, will not renew his contract when it expires at the end of the 2016-2017 season. Instead, he will assume the position of conductor laureate, meaning he will continue in a less-prominent role.

Can Rutter, 59, who helped lead the Chicago Symphony to a new flowering under Riccardo Muti, help revitalize the NSO as a truly top-tier orchestra?

It’s obvious that she has made music a clear priority during the first months of her tenure. Her first major announcement was that the center will join Washington Performing Arts in taking over the festival of American orchestras that ran for four years under the name “Spring for Music” at Carnegie Hall.

Then came the creation of the position of Kennedy Center composer-in-residence, awarded for a three-year term to Mason Bates, a 38-year-old composer who writes compelling orchestral music and also has a flourishing career as a DJ. (“I promise that my world is not focused in this way,” she said, hinting at many nonmusical announcements to come.)

The news about Eschenbach was not entirely unexpected, given that his most recent contract extension last March, for only two years, seemed like an interim solution.

But it does clear the field for Rutter, whose career has been spent running orchestras, to help the NSO reach its potential.

“I think that the role of a music director of an American orchestra today has changed exponentially in recent decades,” Rutter said Wednesday by phone from the Kennedy Center.

A music director has always helped focus the energies of an ensemble of highly skilled players and set the tone for the orchestra’s identity; today, though, there is more to this than simply offering excellent performances of works by Beethoven and Brahms.

“We’re going to be looking for someone who has a fresh [attitude],” Rutter said. “It’s about saying, okay, as we look at orchestras in our world today, how do we remind ourselves of the importance of the historical repertoire, the canon and providing exciting interpretations of that, as well as interacting with music today? What’s the role of the orchestra in terms of community involvement? How are we going to have the orchestra engage across the Kennedy Center?

“An orchestra needs its maestro to be the person to inspire, nurture, build,” she added. Eschenbach “has really given it that.” But, she continued, “it’s better to leave too early than too late.”

In Chicago, Rutter tactfully oversaw the departure of another well-known European pianist turned music director who wasn’t always connecting with audiences: Daniel Barenboim. She was instrumental in winning over the initially reluctant Muti, whose work there has galvanized both players and audiences.

The NSO, one of the Kennedy Center’s crown jewels, has never been able to break into the elite of the nation’s top orchestras. And although Eschenbach oversaw the appointment of no fewer than 15 new musicians — a tremendous turnover — and led two international tours, to South America and Europe, that bolstered morale and won the orchestra new acclaim, he hasn’t consistently built on his successes. Some of his performances have been exciting; others, oddly erratic and willful. While the orchestra is sounding better in some areas, it still has not overcome some of its basic technical problems — such as a difficulty in playing together.

Eschenbach, furthermore, should be held to higher standards. The first person to occupy the joint position of music director of both the NSO and the Kennedy Center, he was, in 2013, the highest-paid conductor in the United States.

His declared income from the NSO of more than $2.7 million, as reported by Kennedy Center tax returns, outstripped colleagues at better orchestras: Muti in Chicago and Gustavo Dudamel at the Los Angeles Philharmonic declared about $1.4 million each that year, while Michael Tilson Thomas earned $2.3 million at the San Francisco Symphony.

It was also about $1 million more than Eschenbach earned from the NSO the previous year, perhaps because the NSO went on tour and he performed a duo recital with the star pianist Lang Lang.

Rita Shapiro, the NSO’s executive director, said that Eschenbach is “differently compensated for tours.” She declined to give specifics.

It’s not that Eschenbach’s tenure has been an unmitigated failure. And he reportedly has a generally warm relationship with the orchestra’s musicians. When the players learned Tuesday that he was leaving, Shapiro said, “It was very quiet.”

What’s been missing, though, has been a clear vision for the orchestra — something that’s become, these days, a requisite part of the job.

Shapiro says that those involved in the music director search — a committee formed of musicians, administrators and, most probably, Rutter herself — will be “spending a lot of time talking about what we need, rather than who we need.”

The NSO has company. This month, both Alan Gilbert of the New York Philharmonic and Edo de Waart of the Milwaukee Symphony announced that they, too, plan to down in 2017, after eight seasons each. The San Diego Symphony is also looking for a music director for 2017-2018.

The NSO is not alone, though, in having a proven veteran such as Rutter on its side.

“The right person for New York or Milwaukee or San Diego or the NSO is not the same person,” Rutter said. “The chemistry in one place is not ever the same chemistry for another. An individual who’s really great in New Jersey is not necessarily really great for another city. . . . What was unique about Chicago was the connection Muti had within the city itself. That’s what we’re looking for: a great musician who feels he can do something in D.C.”

Peggy McGlone contributed to this report.