Airlines currently operating into New York's LaGuardia Airport -- and those that want to -- hammered out an agreement yesterday that paves the way for new operations there this fall by three airlines, including Texas International Airlines.

The agreement, giving TI the right to take off or land at LaGuardia 40 times a day, gives fresh impetus to speculation that TI may be planning service to compete with the shuttle that Eastern Airlines operates as a near monoply on the heavily traveled route between New York airport and Washington's National Airport. TI has not revealed its plans.

Airlines seeking landing rights at limited-traffic airports are prohibited from indicating to the airline scheduling committees their proposed destinations so that incumbents will not keep out prospective competitors.

If a competitive shuttle is in the offing, however, TI is only halfway there. The committee that divides up limited space at Washington National recessed yesterday for two weeks after making little progress in resolving a much more complicated problem that existed for LaGardia.

When the committee started its meetings last month, a total of 18 airlines, including three new to LaGuardia, were seeking the use of 784 slots at the airport. The requests were shaved to 730, well within the 48 per operating hour permitted at LaGuardia. A slot is the industry term for an allowable movement of a plane -- either a takeoff or a landing.

While the airlines were able to reduce the total number of requests for slots to a number that would fit a LaGuardia, getting airlines to move their planned flights out of the 5 to 8 p.m. period provided to be the thorniest problem. Nearly 170 slots were requested for the three-hour period that could accommodate only 144. The "depeaking" process, as the airlines called it, took days.

According to the participants, each airline sees a move out of that popular period in terms of dollars. It disrupts a planned schedule that an airline thinks has traveler appeal and is profitable. An airline may feel a flight moved one hour earlier or later may give a competitor more business, for instance. Also, moving a departure or arrival an hour ahead or behind means moving others as well which has an impact on airplane utilization, ground facilities, employe schedules and work-loads.

In the case of Washington National, the committee is nowhere near fitting the requests into the hours; it first has to whittle down the airlines' requests that will fit within the operating limits set for the airport -- currently 40 an hour between 7 a.m. and 10 p.m. -- by the Federal Aviation Administration. At the end of the committee session yesterday, 23 airlines were seeking a total of 780 slots at National while there is room for no more than 640.

An even greater problem looms for the airlines wanting to operate out of National when the FAA reduces slot availability by another 118 next year under its recently announced revised Metropolitan Washington Airports policy.

The airline representatives who meet are members of a government-sanctioned committee that has been hammering out slot agreements for four congested U.S. airports since 1969. But the Airline Deregulation Act has stimulated new services and increased significantly the number of airlines legally able to fly in and out of them. For years, only 10 airlines operated out of National. In the past, the airline representatives has met repeatedly until they agreed unanimously on the slots for all.

Besides Texas International, other airlines getting the right to operate at LaGuardia for the first time were Midway Airlines and Air North. TI, Air North and Pilgrim Airlines are the three seeking new slots at National.