DETROIT (AP) _ Lee Iacocca will stay in the driver's seat at Chrysler Corp. after his contract expires next year, but the question of his eventual successor will continue to loom large over the nation's No. 3 automaker.

The line to the chairman's office was disrupted last week when Iacocca's heir apparent, Gerald Greenwald, resigned as vice chairman.

The succession issue has heated up at a time when Chrysler's sales and earnings are under the most pressure since the company came back from the brink of bankruptcy a decade ago.

''Right now, there's a battle raging and I'm not going to leave my troops in the field,'' Iacocca said in a statement released Thursday after a Chrysler board meeting in New York. ''We have mutually agreed that my employment will be extended past December of 1991.''

Just how long the 65-year-old Iacocca will continue as chairman and chief executive officer and how much he will be paid isn't known, Chrysler spokesman A.C. Liebler said.

''Iacocca is probably the single most important element ot Chrysler Corporation,'' said Alan Helfman, general manager of River Oaks Chrysler- Plymout h in Houston. ''He sells the sizzle and people like the showmanship.''

That will be a tough act to follow, Helfman said.

''One of my prime responsibilities is to put an orderly succession plan in place,'' Iacocca said. ''We're going to do that according to our own timetable and it won't be driven by a big X on the calendar.''

Greenwald was told by Iacocca about a year ago that Chrysler's chairmanship was ''yours to lose.'' Greenwald chose to lose it, opting instead to head a three-union effort to buy the parent of United Airlines for $4.54 billion.

Analyst Mary Anne Sudol of Fitch Investors Service Inc. said Iacocca probably would stay at the helm for no more than two extra years as a stopgap.

''I tend to think it (the extension) is to give the board time and the contenders the opportunity to establish their own track records,'' she said.

Less than 24 hours after Greenwald's resignation, Chrysler said Robert S. Miller, the company's chief financial officer, would take over Greenwald's title and most of his duties. Chrysler Motors President Robert Lutz got the rest of the duties, but no new title.

The changes prompted speculation that Iacocca might stay on after his contract expires Dec. 8, 1991. Neither Miller, 48, nor Lutz, 58, appeared ready to become chairman in 18 months.

Greenwald was the highest ranking of three executives who announced their resignations in May. Michael Hammes resigned as vice president for international operations to head up hand tool operations at Black & Decker and Treasurer Frederick Zuckerman said he will quit sometime this summer.

Chrysler has been thinning its executive ranks since last October, when it started a $1.5 billion cost-cutting program that will reduce the white-collar work force by more than 2,500 people.

The company reported an 80 percent drop in first-quarter earnings to $71 million. Analysts don't expect an upturn until at least the fourth quarter.

Earnings have been pressured by a dive in the company's car and truck sales. Through the first five months of this year, sales were running nearly 13 percent below last year's pace.

Iacocca signed a four-year contract with the automaker in 1987. He joined Chrysler in 1979 after being fired as president of Ford Motor Co. by the late Henry Ford II.

Iacocca's most lucrative year as chairman was in 1986 when he received $20.5 million in compensation. His average annual compensation since 1985 was $11.5 million. He received $4 million for last year.

The company's 1990 proxy statement says Iacocca will receive 191,250 shares of Chrysler stock this coming Nov. 2 and another 63,750 shares after Dec. 8, 1991.

At $16 a share, Chrysler's common stock price at midday Thursday, the stock would have a combined value of $4.1 million.