Threat of oil drilling fades a bit in Pacific Palisades. Recent political shifts on the Los Angeles City Council may result in veto of proposal to tap oil and gas reserves in scenic cliff and beach area.

After more than 20 years of haggling, a dispute over oil drilling in the well-heeled, coastal community of Pacific Palisades - source of one of southern California's most divisive environmental conflicts - is taking a new twist. Over the years, the Los Angeles City Council has usually voted in favor of requests put before it by the Occidental Petroleum Corporation, the company that wants to plumb for energy in Pacific Palisades.

But now opposition to the project is hardening at City Hall as a result of recent changes in the makeup of the council.

Longtime opponents say they believe the political shift could prove instrumental in seeing that wells are never drilled at the foot of the Palisades cliffs, an ecologically sensitive area near some of the area's most popular beaches.

Company officials, however, play down the importance of the council's current leanings. They claim to still have the momentum in the enduring dispute.

The latest dynamics underscore the Byzantine political nature of modern energy development, particularly in California, where prodigious pools of oil and gas are often found near deep reserves of environmental sentiment. It also reflects the degree to which a ``slow growth'' movement has taken hold in the political structure of a city long identified with unbridled development.

``It seems to reflect a mood change in the city on growth and environmental issues,'' says Joe Scott, publisher of a political newsletter.

Occidental Petroleum believes that up to 60 million barrels of oil and 120 billion cubic feet of natural gas lie in the area. It has proposed drilling up to 60 wells on a 2.5-acre site at the base of the Palisades' eucalyptus-browed bluffs, near Will Rogers State Beach.

In addition to the energy resource, the company says the city stands to collect $200 million in taxes and royalties over the next 30 years if the drilling plan goes forward.

Critics, though, including some Palisades residents and environmentalists, contend the drilling would increase the risk of oil spills and slides along the bluffs and spoil prime beaches. A major slide occurred in the area in 1958.

Occidental maintains that the project is ecologically sound and that modern technologies would allow it to extract the oil with no effect on surrounding terrain.

Two years ago, both the Los Angeles City Council and Mayor Tom Bradley approved a company drilling plan for the area. But the complexion of the council has changed considerably since then, and last week a majority of the members went against the company for the first time in the 20-year battle.

The council voted to ask the California Coastal Commission, which also holds jurisdiction over the project, to reconsider recent approval it gave Occidental for exploratory drilling. Backers of the council move argue that the city's approval in 1985, covering both exploratory and production drilling, is different from the exploration-only application OK'd by the commission. Thus they want it reconsidered.

Although the City Council's vote is considered largely symbolic, it does underscore the political shift at City Hall - and could add momentum to a ballot initiative being considered to defeat the project. Two city councilmen - Zev Yaroslavsky and Marvin Braude, who last year were the authors of a successful no-growth initiative in the city - are weighing a measure for the June 1988 ballot that would ban oil drilling on Los Angeles beaches. Whether the drive goes ahead will hinge in part on the financial backing they can line up.

``The votes are easier than the money,'' says Mr. Braude.

Occidental officials, for their part, appear unfazed by either the council's current tenor or a possible initiative. They note that they already have the necessary approvals from the city to go ahead with the project. They also contend they could win a fight at the ballot box.

``There are currently 17 major urban drilling sites within the City of Los Angeles,'' says Arthur Groman, a lawyer and 30-year member of Occidental's board of directors. ``There is absolutely nothing that distinguishes the Palisades site.''

The fate of the project may be decided in the courts rather than the political arena. In September, the state Court of Appeal is expected to hear Occidental's appeal of a lower court ruling that the city's 1985 ordinance in favor of drilling is invalid.

At the same time, the company faces a related lawsuit filed by No Oil Inc., an activist group that has long fought the project.

Both sides believe they are on firm legal footing. And Occidental's Mr. Groman says that, with a favorable Court of Appeal ruling, exploratory drilling equipment could be on site by January.

But opponents contend that derricks will never inhabit the site.