London — What do you do if you have an elephant that water-skis? A sea lion starring in a television film? A grain of rice with portraits of Queen Elizabeth and the Duke of Edinburgh engraved on it? A beard so luxuriant that you are a member of the local ''whiskers club''?
What do you do if you have tried to gain publicity for your golf club by offering large prizes for holes in one? Or you are a house builder and you offer a house to anyone who can guess the combination of a safe in which the deeds are locked?
Or you are an Oxford scholar who wants to sail from Ireland to Newfoundland in a leather boat to test a hypothesis that an Irish monk did it 1,400 years ago? Or you are preparing to make the first man-powered flight across the English Channel in the pedal-driven Gossamer Albatross?
Answer: You call Lloyd's of London.
These are the kinds of insurance risks on which Lloyd's has built a reputation for speed, flexibility, and the ability to assess tricky situations.
They make up only a small part of Lloyd's $4 billion worth of premium income a year. But they help form the reputation Lloyd's is fighting to protect today in the face of a wave of malpractice allegations now forcing changes in the way the Lloyd's market operates.
The waterskiing elephant was insured when it teetered into public view at the Windsor Safari Park in London. The sea lion was the star of a British television program called ''Animal Magic.''
The royally decorated grain of rice was insured for $20,000 by a Lloyd's broker. Another covered the beards of a Derbyshire ''whiskers club'' for $:20 ($ 32) apiece - against fire and theft.
The hole-in-one policy started off badly. One broker wrote a policy without seeing the club involved, which was in Australia, basing it on an educated guess on how many tee shots would be hit per year and other factors. The club, however , shaped one of its shorter-hole greens like a saucer, delighting players who saw their tee shots slide gently into the hole.
Lloyd's was less pleased. From then on it made sure that hole-in-one insurance was granted only on approved courses.
Some film actresses gain publicity by insuring themselves extravagantly - Betty Grable, for example, boasted ''million dollar legs.'' More unusual was a composer, Richard Stokler, who insured his ears.
On another side of show business, the sea gull that starred in ''Jonathan Livingston Seagull'' was also insured at Lloyd's.
More straightforward is insuring cars (such as a 1933 Aston Martin driven from Paris to Turin in a rally by Stirling Moss in 1978), jewels (the $5 million ''premier rose'' diamond when it was en route from South Africa to New York), and trains (the private owners of the ''Flying Scotsman'' and others have insurance when the engine pulls special trains here).
Sports figures with Lloyd's policies at one time or another include Bjorn Borg, the soccer star Pele, and entire US basketball, baseball, ice hockey, and football teams. Sources recall that Lloyd's, well accustomed to insuring professional stuntmen in real accident prevention films and commercials, had little difficulty in covering former champion skier Jean-Claude Killy in a commercial film.
Killy was to ski at high speed down a mountain, pursued by an ''avalanche'' controlled by carefully timed explosives in the snow. But the avalanche was started too early and Killy had to go flat out to escape. It was a narrow escape for Lloyd's as well.
The ability to assess risk, and to impose conditions, is essential to a Lloyd's underwriter. A few months ago, a young Merchant Navy officer wanted to sail from Dover to Cap Griz Nez in France in a bathtub. He wanted $:100,000 ($ 160,000) in third-party liability - and he found it, on one condition. The plug had to stay in position at all times.
Brokers are not fools. If someone offers to pay a premium of more than 15 percent of the sum to be claimed, brokers tend to shy away. Premiums of less than 10 percent are standard.
If they can assess the risks with a fair degree of accuracy, however, they are likely to issue cover. Film stars usually insure themselves for large amounts, and Lloyd's goes along. The highest-valued star of recent years was Christopher Reeves, the star of ''Superman.'' During the filming of the first film, the studio took out a policy on him worth $20 million.