Harry Teter Jr., president for the past nine months of the board of trustees of the nonprofit New National Theatre Corp. (NNTC), will resign on April 1 to accept a position as the National Theatre's new managing director.

The announcement was made yesterday after a meeting of NNTC, which runs the theater, and officers of the New York-based Shubert Organization, which provides the bookings. Teter's new job, which falls under the jurisdiction of the Association of Theatrical Press Agents and Managers(ATPAM), carries an annual salary of "$45,000 and up," according to Gerald Schoenfeld, chairman of the Shubert Organization. The as-yet unnegotiated salary will be paid by the Shuberts.

Replacing Teter on April 1 as the president of NNTC's board, a non-paying post, will be Dr. Donn Murphy, currently vice president. Sterling Tucker will function as the new vice president, while Joseph S. Fontana has been named secretary until NNTC's annual elections in November.

In his new post, Teter will be the Shuberts' on-the-spot representative in charge of general operations. But he said yesterday that "I want to see that the advantages of having the Shuberts at the National also benefit as many other theaters in the area as possible. We have a duty to the National, but also a duty to help the community." Teter, a lawyer, intends to keep his law office open.

Teter's appointment mends a longstanding breach between NNTC and the Shuberts, who for more than two seasons were unable to find a mutually acceptable candidate for the position of general manager, now called managing director. Schoenfeld described the current working relationship as "very amicable."

The National has been closed since spring for extensive renovations. James C. Crozier, executive vice president of Quadrangle-Marriott, the development corporation doing the work, told the board yesterday that the improvements should be completed on schedule, by "late October or early November." Noting it was too early to talk of an opening show, Schoenfeld said that two possibilities were the blockbuster musicals "Dreamgirls" and "42nd Street."

NNTC also plans to redecorate the theater for a gala reopening and last October accepted a $1 million interest-free loan from the Shuberts to cover the costs. In return, NNTC gave the Shuberts a 20-year contract to book the theater.