The monthly statement to some Visa account customers of Rhode Island's Industrial National Bank carries a reminder when their driver's licenses are about to expire.

Customers who hold the bank's Westminster Visa debit card can use their account for transactions as diverse as stock purchases and utility payments. To be eligible for the special card, the customer must have assets of $150,000 in the account and pay an annual fee of at least $500.

The Westminster Visa plan is an example of the way credit card distributors are aggressively expanding their activities to win a place in the emerging "financial supermarket"--where an array of financial services are available under one roof. With their direct links to the consumer, credit and debit cards are likely to be a major part in the development of the financial supermarket. (Debit cards allow for direct withdrawals from funds maintained in cardholders' accounts.)

Not only are the card companies increasing their bank-type activities, but also, in their scramble to reach the top of their industry heap, are offering a variety of offbeat or nontraditional services, such as reminding customers to renew their driver's licenses. In the New York suburbs, some Visa cards can be used to make alimony and child-support payments. American Express bills more than 100,000 of its customers monthly for their MCI Communications Corp.'s long-distance telephone service.

"The upscale executive is very interested in having sophisticated financial services delivered in a hassle-free, convenient fashion," said Pie-Yuan Chia, senior vice president in charge of Citicorp's travel and entertainment cards, Diner's Club and Carte Blanche. "The question is only how fast and what way."

But William M. McCormick, president of American Express' Financial Services Group, is cautious in predicting how far the card industry can go in bringing new services on line. Certainly, he and others note, the technology exists to permit consumers to pay all their bills through their cards.

"I can see more and more centralized payment systems developing," he said. "The system will do a lot of work that people used to do themselves. The question is what do consumers want and what are they willing to pay for."

For now, American Express is the prime target as other credit card companies attempt to attract prosperous consumers, particularly business travelers. But the target isn't standing still.

"We basically want to be the leading financial services company in the world," noted Sanford Weil, chairman of the executive committee of Shearson/American Express. This summer, the company will begin offering its Financial Management Account, which will link its credit card operation with its Shearson brokerage subsidiary.

The new plan, modeled after the Cash Management Account offered by Merrill Lynch, Pierce, Fenner & Smith Inc., will enable participants with $25,000 or more invested to purchase mutual funds and other securities through their account. Payments owed for purchases through their American Express Gold Cards will automatically be withdrawn from their balances. Other brokerage firms, such as The E. F. Hutton Group Inc., also will participate.

Meanwhile, the so-called bank cards, Visa and MasterCard--with a combined total of 10 times as many cards in circulation as American Express--have, in concert with affiliated banks, launched their own premium cards, modeled on the American Express Gold Card. And Sears, Roebuck and Co., the nation's largest retailer, and Bank of America, the nation's largest bank, are each reportedly considering major new thrusts into the credit card business.

"There's no question that the competition is heating up," said McCormick of American Express. "They are moving into the travel and entertainment sphere and there is less difference in the utility of the cards than there was." (Originally, bank-affiliated credit cards were intended for retail installment purchases, while travel and entertainment (T&E) cards, which require payment within 30 days of billing, were for transportation, dining and lodging charges.)

"Our sense is that neither of the so-called premium bank cards even begin to stack up against the American Express Green Card, let alone the Gold Card," an American Express representative said. "We focus on a small, select customer group in which we have the preeminent reputation and market position," Louis V. Gerstner Jr., vice chairman of American Express, boasted in a recent speech.

Perhaps the most visible sign of the new competition in the credit card industry is the multimillion-dollar promotion effort by Citicorp--the nation's second largest bank, and the most profitable--for its Diners Club card, an operation it purchased last year.

Its national advertising campaign depicts a well-dressed man sitting comfortably in a first-class airplane seat, while the card is touted as the one "designed for the people who use it most."

"We have a fairly good product that even seems stronger than American Express overseas," said Citicorp's Chia. "But the product suffered from a lack of awareness of it in the marketplace. People didn't know what Diners Club is. We're obviously positioning it to the high end of the market, to the upscale business crowd that takes shorter trips and use T&E cards more often."

Citicorp also is using a number of promotions, such as gift certificate giveaways, to try to build a base from the 4 million combined worldwide distribution of Diners Club and Carte Blanche, and is offering restaurant meals or airline credits to customers whose bill exceeds their normal monthly purchases with the card. Citicorp officials will not give specific numbers, but industry observers say Diners Club has only about 600,000 domestic users, and the business has fallen off sharply in recent years.

Meanwhile, MasterCard is launching its own upscale card, and Visa International, through its 13,000 affiliated financial organizations, launched a campaign in April to market its premium cards. Visa, with about 95 million cards worldwide, is traditionally considered a bank card, as opposed to a T&E card, but is now offering features like travel insurance and a hotel reservation service in its effort to bite into American Express' business.

"The time is right and the market is right," said Richard Rossi, public relations manager for Visa International. "We want to displace American Express as No. 1 in that market within about five years."

Already, Rossi said, the new premium Visa card has commitments from 70 domestic banks and more than 30 abroad. Visa hopes to have one million of the cards in circulation by the end of 1982, a figure that they project will double by 1984. "We think that whether the market can support five or six cards or only two, we are in a position to be among them," Rossi said.

As Rossi's remark suggests, the question of how many of the credit cards can survive lurks in the background as the competition intensifies.

"I don't know if there is enough room for all those cards," said Jack Cox, whose firm, AECS Ltd., does economic consulting for the industry. "But I certainly think there's room for two major cards.

"The problem is they are all shooting for the same upscale market," he said. "Sometimes I think there are more financial institutions than upscale people."