The Soviet military: Will the brass get more polish or lose its luster?

He stood to the right of Konstantin Chernenko, the new Soviet leader, during the funeral of Yuri Andropov. But, then, he had stood to the right of Yuri Andropov for the funeral of Leonid Brezhnev only 15 months earlier.

He sat in on a meeting between Chernenko and leaders of the Warsaw Pact nations.

But, then, so did other Soviet officials.

He is Dmitri Ustinov, the 75-year-old Soviet defense minister. A number of diplomatic analysts - as well as some Soviet sources - indicate he played a key role in engineering the ascendancy of Andropov over his erstwhile rival, Chernenko.

Now that Chernenko is at the top of the Kremlin hierarchy, analysts will be trying to gauge Ustinov's influence. And it is from such clues as his proximity to Chernenko at official functions that most of the evidence will come.

It is more than a matter of abstract Kremlinology, more than merely a study of personalities.

Many analysts say that under Andropov - and perhaps under Brezhnev during his last years of rule - the Soviet military gained in prominence and power. Twice - during the aftermath of the shootdown of Korean Air Lines flight 7, and during the debate over the stationing of new NATO missiles in Western Europe - Marshal Nikolai Ogarkov, the chief of the general staff, held press conferences to explain the Soviet position. Such a public role for the military was virtually unprecedented in this country.

And Western analysts say the trend has broad implications on a variety of issues - among them, Moscow's willingness to enter into arms control agreements, its attitude toward East European nations which act as a military ''buffer zone'' for the Soviet Union, and the Soviets' proclivity to project their military power into trouble spots such as the Middle East, the Caribbean, and the third world.

For these reasons, Western analysts here are watching closely for signs of the military's future role.

Early indications - and it must be pointed out that they are highly speculative - are that Chernenko's ascension was something of a setback for the military and for the Committee for State Security (KGB).

The preliminary assessment by some Western analysts is that it represented something of a counterrevolution, a move by the Communist Party to reassert its own primacy after the military and KGB played a decisive role during the last succession. Andropov headed the KGB for 15 years.

Yuri Andropov, with military and KGB backing, conducted a crackdown on sloth and corruption in the party. For example, fully one-fifth of the party's regional secretaries were replaced during Andropov's brief tenure.

That apparently did not go down well with old-line party members, who had grown comfortable under Leonid Brezhnev's 18-year rule. Brezhnev espoused a policy of ''respect for cadres,'' which, in practice, meant lifetime sinecures for key party officials. Chernenko, a Brezhnev protege, might be counted upon to reinstate that policy.

Such theories are, of course, mostly conjecture. And they are clearly preliminary, since not much information is currently available.

Some Soviet sources, however, never even accepted the premise that the military's influence was on the rise. As evidence, they pointed to the numbers.

''The military have not increased their presence in the Politburo, the Central Committee (of the Communist Party), or the government,'' a key Soviet analyst said before the succession.

American observers disagreed, arguing that it is influence - not numbers - that counts in this society.

''The military has gained a certain accretion of political power,'' said a ranking American diplomat a week before Andropov's death.

But, he added, ''I don't think it means (they're) headed toward a military rule.''

Indeed, that was never seriously suggested by Western analysts. And Soviet sources repeatedly belittled the idea of a growing role for the military.

''In this society,'' a Central Committee member said, ''it is the party that plays the leading role. The military has a role, but it is not independent of the party.''

Still, analysts will be watching carefully for signs of the military's role under Chernenko. But even if the military's standing were clear to Western analysts, the implications of that knowledge are decidedly unclear.

Asked if the Soviet military was advocating extremist positions - or, alternatively, pushing for moderation during negotiations with the United States over nuclear issues - the diplomat replied, ''That's an open question.''

The same can be said for much of what is going on behind the Kremlin walls as Konstantin Chernenko takes control.