Former prime minister Joe Clark, flying high in the opinion polls but disliked within his own party, is struggling to stay in position for a chance to regain power in Canada's next national election.

Clark, 43, leader of the right-wing Progressive Conservative Party, managed to last only nine months after becoming prime minister in 1979.

In a heated political atmosphere generated by predictions of current Prime Minister Pierre Trudeau's retirement, Clark's stubborn quest for another try has become a personal drama of national scope. On its outcome may depend the Conservatives' chances of unseating Trudeau's long-dominant Liberal Party when Canadians next go to the polls.

The issue of Clark's leadership will come to a head at a three-day Conservative convention starting Wednesday in Winnipeg at which Clark will have to brave what amounts to a confidence vote by the 2,000 delegates.

Clark's fate is intricately tied to that of Trudeau. The Liberal leader, reelected at Clark's expense three years ago, has until 1985 to dissolve the current Parliament. But Trudeau has said he will not run for office again, and some observers expect him to step down and clear the way for an election in the next year or so.

The Conservatives, who hold 102 seats in the House of Commons against the Liberals' 146, have gained momentum from deep public anger over the economy, which last year fared worse than any other in the industrialized world.

Canadians' approval of Trudeau's leadership, as measured by opinion samplings, has slid under 30 percent, low enough to worry many Liberals about the future of their party.

Conversely, Clark received a 49 percent approval rating in the latest Gallup poll, taken in December. But rather than bring unity to the traditionally fractious Tories, this surge in popularity appears to have intensified the efforts of the anti-Clark element in the party.

That faction argues that Clark won the 1979 election mainly because of the public's rejection of Trudeau, then in office almost 11 years. Now, despite the Tories' current lead, the dissidents say Clark could still lose at the polls to a fresh Liberal candidate once Trudeau quits.

As a result, the country has been subjected to a spectacle of back-biting and discord in the Tory ranks, fought out in full fury in the media in recent months. Apparent new lows in debate have been reached, such as when one Conservative member of Parliament likened Clark's popular image to "the dog food that won't sell."

Insults, however, are nothing new to Clark, who has been the whipping boy of Canadian politics for years. His almost total lack of mystique led one critic to label Clark's style "reverse charisma."

Pleasantly engaging in private, Clark on stage is embarrassingly awkward, as though unable to overcome the small-town shyness of his boyhood in High River, a town of 2,000 residents south of Calgary in the western province of Alberta.

He often comes across stilted and pompous, and some of his utterances--such as when, on visiting an Indian village, he asked, "What is the totality of your land?"--have entered Canadian folklore.

"Sure it hurts," Clark has said of his abusive press reviews. "It's a great irritant . . . but there's no use in fighting back. No one wins. The media always have the last word."

Clark, a failure at law school and with no job experience, advanced in politics over intimidating odds. He was once described in his early Ottawa days as "some foundling left on the steps of Parliament," and was greeted with headlines saying "Joe Who?" when he unexpectedly won his party's top position at a divided 1976 leadership conference. But personal toughness, a renowned desire for power and a highly regarded talent as a back-room organizer have always carried Clark forward.

On the opposition benches since 1980, he has won widespread praise in successful battles to force changes in Trudeau's sweeping energy legislation and proposals for constitutional reform.

"My position is 100 percent clear. I'm the leader of the Progressive Conservative Party and I intend to stay and be a Progressive Conservative prime minister again," he has declared.

In a country seemingly disillusioned with the rapidly expanding role of government under Trudeau, there is great acceptance of Clark's conservative message. Like President Reagan, Clark favors increased investment incentives for business. And he wants government bureaucracy to be partly dismantled, although Clark's cutbacks would not extend to trimming welfare and other social programs, as some Tories urge.

If reelected, Clark says, he would alter Trudeau's nationalistic energy program, which he says "has just sent tremors of fear throughout the economy because nobody can plan if you think the government is going to act retroactively or confiscate" company assets. Trudeau has sought to bring oil investments under Canadian--rather than largely American--ownership.

Also in need of reform, Clark says, is Ottawa's restrictive policy on other foreign investment, a Trudeau plan that incited resentment among business, the leaders of Canada's provincial governments and the Reagan administration.

Clark's biggest problem is his record as prime minister in 1979. The Conservatives' minority government was marked by glaring political miscues and muddled planning in Parliament that finally led to the party's downfall.

The delegates in Winnipeg, as required by a party by-law, must vote on whether to hold a leadership conference at which Clark would be challenged by other aspirants. Despite a Tory delegates' revolt centered in Toronto, Clark is expected to obtain the 50 percent vote of confidence needed to avoid a leadership race.

But the crucial question is whether he can win approval of roughly 70 percent of the delegates, the level considered necessary to forestall a long-term split damaging both to Clark and his party.

"I'm just about despairing," said one party strategist. "Except for a miracle, Clark can't do well enough. And if he doesn't, all the business left unfinished by the convention will be carried on and on."

One Tory member of Parliament said, "I've become a fatalist. Here are Canadians desperately searching for an alternative, and here we are about to decapitate ourselves."