The Mashantucket Pequots, a small and obscure Connecticut tribe, won the right to establish casino gambling on their reservation in Ledyard based in part on a provision in the 1988 Federal law that any form of gambling otherwise allowed in the state must be permitted on a reservation.

Since Connecticut allowed churches and civic groups to hold so-called "casino nights" at which casino-type gambling was conducted, the tribe maintained, and the courts agreed, the tribe could build and run a full-fledged casino on its lands.

In the wake of the decision, which was ultimately upheld by the Supreme Court of the United States, other tribes have rushed to get into the gambling business. At present, at least 61 tribes in 18 states have opened 100 casinos. Just three weeks ago, New York's Governor, Mario M. Cuomo, gave approval for the Oneida tribe to open a $10 million casino it is building 30 miles east of Syracuse.

Nationwide, Indian gambling enterprises, including bingo, do $6 billion a year in business, twice the total of Atlantic City's casinos. Mounting Competition

Faced with such mounting competition, Atlantic City and Mr. Trump, its biggest player, have become increasingly concerned, and the new suit is regarded as evidence of that concern.