Secretary of State George Shultz is pushing a controversial diplomatic parlay that links the proposed intermediate-range nuclear treaty (INF) to a major reduction of violence and battle in East-West ''regional conflicts'' just as those conflicts are costing the Soviet Union heavily.

The death of former CIA director William Casey handed Shultz new freedom to press Moscow for political solutions to defuse Reagan Doctrine conflicts in Nicaragua, Angola and Afghanistan. With the conciliator Howard Baker running the White House and the National Security Council staff recovering from Iran-contra, Shultz is now freer to put his linkage parlay -- the ''Shultz Doctrine'' -- on fast forward.

But fast as it may be, the track is by no means clear. Shultz's defeat in making his ace diplomat Philip Habib the chief U.S. negotiator in the Nicaraguan peace moves showed Baker's sensitivity to pushing President Reagan too far too fast. When the Republican right rebelled on grounds that Shultz and Habib were overly eager for Nicaraguan peace, Shultz bowed without wasting time fighting for his chief diplomat, and Habib resigned.

Although the general line of Shultz's linkage parlay is growing bolder, there have been other setbacks as well. One was the failure of a psychological warfare gambit reportedly considered against Pakistan President Zia ul-Haq. Pakistan is the transit point for Stinger anti-aircraft missiles and other arms for the mujaheddin. These weapons gave the Afghan freedom fighters a stunning victory this summer: perhaps 300 Soviet spetsnaz (special forces) killed and 15 aircraft shot down.

The psychological gambit was a tough anti-Pakistan congressional resolution criticizing Zia's nuclear policies that was scheduled to pass one day before Undersecretary of State Michael Armacost's arrival in Islamabad early this month to confer with Zia. One purpose of the resolution, diplomatic sources told us, was to make President Zia more amenable to U.S. ideas for toning down military actions in Afghanistan a bit. That would presumably soften the Soviet position on a political settlement of the war and achieve an end to the Soviet occupation.

But senators rebelled against such tactics. Just before the resolution was voted on, a large phalanx led by conservative Republicans gained a significant ally -- Democratic Sen. Bill Bradley. With the aid of Bradley, a strong supporter of the anti-Soviet mujaheddin, the resolution was softened by including a mention of India's nuclear activities and removing some harsh implicit criticism of Zia. Thus the ploy was dead before Armacost's arrival in Islamabad.

Shultz is praised at State for stalwart support of the Reagan Doctrine. In fact, however, he has never been a conspicuous player. Middle-of-the-road Rep. Robert Michel, the House Republican leader, chastised him in an extraordinary letter almost two years ago for his opposition to a mere $27 million in nonlethal assistance to Jonas Savimbi's anti-Soviet UNITA movement in Angola. The confidential letter warned Shultz that if the United States said no to Savimbi on grounds that giving aid would hurt the negotiating track, as Shultz argued, that argument would ''come back to haunt us'' in any future similar case involving the anti-Soviet Nicaraguan contras.

Shultz lost that battle, just as he has now lost Habib. He also failed, according to Republican senators backing the Reagan Doctrine, to carry his case against sending Stingers to both the Angolan and the Afghan freedom fighters.

But hard work is being done inside the State Department to further the Shultz Doctrine of linkage. The policy planning staff circulated a paper recently blaming the United States for not being imaginative enough in thinking up ways to persuade Moscow to stop cheating on nuclear treaties.

A new paper now making the rounds asserts that ''trust'' is probably the single most important ingredient for developing U.S. confidence that an INF treaty will not also be violated. It suggests that such trust depends on the appearance of a better U.S.-Soviet relationship overall. The paper says that the key to reforming that relationship, in the words of one official who has read it, is correct ''management of Soviet perceptions'' of U.S policy. Translated, this approach argues that political solutions to regional conflicts would convince Moscow that the feared and hated Reagan Doctrine is ending.

The Shultz Doctrine goes beyond regional conflicts. President Reagan's choice of C. William Verity Jr. as secretary of commerce sends a strong signal of more U.S.-Soviet trade, which Moscow desperately wants and needs. Verity, a Shultz favorite, was cochairman of the U.S.-U.S.S.R. Trade and Economic Council from 1977 to 1984.

In the offing lie other linkages that Shultz believes could usher in ''trust'' and detente built on the same foundation that briefly supported the Nixon detente but then collapsed under the weight of reality: nuclear pacts, trade and financial goodies. That could not have been imagined, much less glimpsed, when the Reagan administration came to town nearly seven years ago.