On the day after the death of Soviet President Leonid Brezhnev was reported, the tabloid New York Post used most of its front page to display the bold, black headline: SINISTER KGB BIGGIE GETS BREZHNEV JOB

Shades of the Cold War. We have, it seemed, stepped far back into the dark past. Heaven help us if that is the sort of response Americans make to the fateful period of change now beginning.

While the death of Brezhnev comes at a delicate moment in Soviet-American relations, it holds at least as much promise as peril if we choose to seize the opportunity.

Both countries are reexamining their defense policies, and those debates over military strengths and capabilities promise to grow more intense. Both are facing hard economic realities that require new approaches. Both are entering a political period that forces them to assess experiences and look with more than normal introspection at policies that have brought them to this point.

The question is whether each side can profit from that internal kind of examination.

Americans again are pondering the lessons of the Vietnam war. Television screens and front pages carry daily reminders of the cost of that commitment in human suffering. Inevitably, they raise fresh questions about the cause for which we fought and premises on which it was based.

Once more, our political process has shifted the nation's course. In a relatively short span, voters have flirted with, if not embraced, a more sharply ideological approach to national affairs. Now, in a remarkably uniform expression across the country, they have rejected all elements of extremism. They clearly have directed political leaders to get on with the practicalities of problem-solving and put aside notions of forming new ideological groupings to govern the country.

This change comes after an unprecedented era in which the nation's political leadership has changed repeatedly. The office of president, once the most stable in the western world, has seen a parade of one-term chief executives.

Along with this rapid presidential turnover, the nation's foreign policy leaders have been succeeding each other in bewildering procession.

In the 18 years since the Gulf of Tonkin resolution made Vietnam an official U.S. conflict, the United States has been led by Lyndon B. Johnson, Richard M. Nixon, Gerald R. Ford, Jimmy Carter and Ronald Reagan, who are about as different in personal temperament, political viewpoint and geographical background as the country can produce.

Yet all have had to deal with the same questions involving relations with the Soviet Union and the communist world and what to do with Vietnam-type conflicts. The same can be said of the seven secretaries of state who have set the foreign policy course over that period: Dean Rusk, William P. Rogers, Henry A. Kissinger, Cyrus R. Vance, Edmund S. Muskie, Alexander M. Haig Jr. and George P. Shultz.

The contrast with the Soviet Union could not be more striking. Only one leader has held absolute sway over Soviet destinies since the formal Vietnam war period began in 1964. Leonid Brezhnev has been the man with whom our presidents and policy-makers have dealt every year since then, and standing behind him has been essentially the same Soviet leadership structure that has guided the Soviet Union since World War II.

Foreign Minister Andrei Gromyko, for instance, provides a constancy that in the United States would be astonishing. He led the Soviet delegation at the San Francisco conference that created the United Nations in the fall of 1945; he sat beside John F. Kennedy in the White House and lied about the secret installation of missiles in Cuba 20 years ago last month, and he still brings word of Soviet intentions to our present chief executive and secretary of state.

Brezhnev's death thus signals more than a change at the top. It marks the beginning of the passing of the Soviet leadership establishment that has ruled for two generations. These are the people forged by World War II and hardened by Cold War antagonisms. They have learned to live uneasily with a tenuous arm's-length relationship with the United States and the West.

Waiting to assume leadership is a younger group to whom Stalingrad and the memory of more than 20 million fallen Russians in World War II are only historical footnotes, not personal experiences that dictate tempered lessons about war and peace. These new Turks face very different questions. They confront a Soviet Union whose economy grows weaker, whose military leadership is challenged by a new arms race that will further drain its country's resources and whose forces are stretched thin on borders from Poland to Afghanistan.

Whenever it assumes command, the new leadership will face a period of great stress. Not the least of the challenges, of course, is to fashion a new relationship with the United States.

Perhaps it is too much to hope that the new spirit of political realism now seen here will translate into improved Soviet-American relations and an easing of world tensions. But in another sense there is reason for hope.

One of the most interesting aspects of the midterm election campaign was the unanimity with which politicians and voters agreed about defense spending. In other campaigns, calls for increased defense spending were nearly always applauded. Strengthening America has been a potent political theme, but not this time. Candidates of both parties were telling the voters they favored slashing defense spending. This year, that stand won votes.

The nuclear freeze issue, though not a dominant factor in the election, nonetheless carried a national message when voters in eight of nine states approved such a proposal.

This suggests that the climate exists for a new, positive approach on arms control to the emerging Soviet leadership. It would be in both nations' interests, and the United States has nothing to lose. The choice is simple and stark: neither society can afford to keep pouring its national treasure into greater and more destructive armaments, especially in a time of growing economic strain.

Each would profit from a mutual scaling-down. Then each could begin to put its full energies to more productive endeavors such as were suggested long ago by one of the greatest scientists of his day.

At the end of the 19th century, Sir Thomas Huxley visited the United States. As he was about to return to England, reporters on his ship peppered him with questions. Wasn't he impressed with how big and powerful and rich the United States was? Wasn't he impressed with the signs of material prosperity, growth and wealth he had seen on his journey?

Huxley fixed his questioners with an icy stare and replied:

"I cannot say that I am in the slightest degree impressed by your bigness, or your material resources, as such. Size is not grandeur, and territory does not make a nation. The great issue, about which hangs the terror of overhanging fate, is what are you going to do with all these things?"

That remains the question U.S. and Soviet leaders have yet to answer.