In a move of potentially major significance for U.S. efforts to check the spread of leftist influence in the Caribbean, Guyana's socialist government has agreed to adopt a conservative economic austerity program recommended by the International Monetary Fund.

The decision means that Prime Minister Linden Forbes Burnham's government will have to put the brakes on its drive for collectivization of the Guyanese economy and start following policies more sympathetic to private investment and the attitudes of the international banking community.

In terms of its broader political significance, the move may increase the tensions in Guyana's relations with the two other strongly leftist governments in the English-speaking Caribbean -- Jamaica and Grenada.

In the past, the three governments have taken a pro-Cuban, anti-American line that had caused them to be regarded collectively as the potential cutting edge for President Fidel Castro's efforts to extend Cuba's influence through the Caribbean.

But more recently, Burnham has shifted toward the right in ways that have strained his ties with the two island repulbics.

His acceptance of an IMF austerity program is in stark contrast to the action of Jamaica's Prime Minister Michael Manley, who chose to plunge his country into financial chaos last March rather than accept the constraints the IMF wanted to impose on his economic policies.

Guyana's decision became known during the annual meeting here this week of the Caribbean Group for Cooperation in Economic Development, organization of Caribbean countries receiving outside aid, the nations dominating the aid and multinational lending agencies.

In exchange for accepting the austerity program, Guyana will receive IMF standby credits of roughly $100 million over three years to help resolve financial and economic problems. Reliable sources yesterday said the final details of the accord are being worked out and are expected to be announced in July.

Even more important to Burnham than the standby aid is the austerity program's role in helping him toward realization of his dream of building a massive hydroelectric power and aluminum-smelting complex in northwestern Guyana.

That plan, known as the Upper Mazaruni project, is regarded by economists as having the potential to transform the economy of Guyana, a former British colony of 850,000 persons on the northeast coast of South America, by greatly reducing its dependence in imported energy and allowing it to cash in more on its vast bauxite resources.

But while the World Bank has pronounced the project feasible, it had made clear to Burnham that there would be no possibility of putting together the financing -- estimated at $11 billion to $2 billion -- unless he pursued economic policies that would to attract private foreign investors and satisfy the stringent conditions of the multinational lending organization. a

Burnham, Guyana's leader since it gained independence in 1966, long had followed a leftist path of nationalizing foreign holdings, bringing the major components of the economy under government control and even renaming the country the Cooperative Republic of Guyana to underscore his aims.

Recently, though, Burnham's desire for the hydroelectric project and the pressure of mounting internal problems have spurred him to move away from his devotion to radical rhetoric and ideas.

Instead, he has sought to project a softer image to the international business community through guarantees for private investment, talk of joint ventures with foreign companies and most dramatically his acceptance of IMF fiscal doctrine.

To meet the standards called for by the IMF, Burnham will have to make major spending cuts through the politically risky steps of raising the cost of electricity and urban transportation and lifting subsidies designed to hold down the price of rice, a major staple of the Guyanese diet.

To encourage him along this course, World Bank officials yesterday said that the bank has decided to loan Guyana approximately $23 million to be used partly for studies on the feasibility of the hydroelectric project.

In reviewing the Caribbean group's meeting, which ended yesterday, Nicolas Ardito Barletta, vice president of the World Bank, said collective aid pledges to the region are expected to rise during the coming year, although he added that a tabulation of the pledges has not yet been compiled.

The organization, founded in 1977, resulted partly from U.S. efforts to spur greater regional cooperation in the Caribbean. Aid pledges from donor nations and agencies jumped from $220 million in 1977 to $612 million last year.