The Civil Aeronautics Board granted seven airlines new routes yesterday, linking Puerto Rico and the Virgin Islands with several Northeast cities, including the Washington area.

Effective today, Allegheny Airlines, American Airlines, Eastern Airlines, North Central Airlines, and Evergreen International Airlines, a charter airline, get new scheduled route authority from the Washington-Baltimore area airports to San Juan or the Virgin Islands or both.

Those five airlines, along with Northwest Airlines and Trans Carib Airlines, also got routes variously connecting Bostun, New York/Newark, and Philadelphia with the Caribbean points.

In another major development, U.S. officials announced the signing of a new air services agreement with Australia that calls for new low, scheduled air fares between the two countries and receptive conditions for charters.

Although the bilateral is not as liberal as others recently signed by the United States, the agreement is considered "quite a breakthrough," according to one aviation official, given Australia's past intransigence to U.S. liberalizing initiatives.

The new agreement also facilitates the start-up of new air service by Continential Airlines to Sydney from Los Angeles on May 1.

Under the agreement, each country agreed not to turn down new airt fares of airlines for passenger traffic that originates in the other country, if the originating country's aviation authority approves them. U.S. officials be- lieve the provision will allow fares for one-way or round-trip tickets purchased her to drop significantly.

Continental, for instance, has proposed to offer a roundtrip ticket to Australia from Los Angeles for $760 with a 30-day advance purchase provision; the lowest fare for an individual ticket has been $1,055. Continental also plans to cut the regular coach ticket from $1,642 to $1,348.

Quantas has proposed a 41-day, advance-purchase ticket for off-peak travel season (spring and fall) for$315 roundtrip from L.A. to Sydney, compared to the $1,026 the same ticket costs in peak season.

Pan American World Airways, which already has a U.S.-Australia route, has proposed a $740 budget fare.

In an exchange of letters, both governments agreed they would approve with "minimum administrative requirements and formalities" various kinds of charters, although the Australian would not agree to let in U.S. public charters with their minimal restrictions.

In other actions:

The CAB said it would grant exemptions to any airlines that want to start service into Oakland, Calif.'s airport, or into Chicago's Midway Airport from a number of large cities, in order to get more airline service into the underutilized airports.

Seaboard World Airlines filed an appeal with the U.S. Court of Appeals here yesterday after the CAB gave Tiger International authority to increase its holdings of stock in Seaboard to 25 percent. The stock must be put in a nonvoting trust that would insulate the carrier from control of the other while a CAB hearing explores the legality of the acquisition. Tiger now has 15.6 percent of Seaboard's stock. Tiger said it is proceeding with necessary filings to carry out a previously proposed tender offer for 580,000 shares of Seaboard's common stock.

The board that operates the San Diego Airport voted not to let any new airline into the airport for a one-year period, giving noise abatement as the reason. Federal officials are studying the action to determine whether it is legal under federal noise standards and the recently enacted airline deregulation measure, sources said yesterday.

The action apparently did not bar airlines now operating into the San Diego Airport from increasing their operations, presenting possible anticompetitive problems, according to one sources.