Sunday coupon-clippers alert! Dart Drug Corp. is moving into the cut-rate legal services market. The drug store chain, with more than 50 stores in the D.C. metropolitan area, plans to open three legal clinics by next week in stores in Fairfax, Manassas and Arlington.

Dart has a lease arrangement with a Northern Virginia law firm in the process of being formed by Mark Zilberberg, Gregory Wade and Vincent Fuller Jr., who will operate the three clinics as branches of their Vienna office.

The space, formerly occupied by an optometrist, is Dart's. The risk and headaches belong to the lawyers, who have pooled "a couple hundred grand," according to Zilberberg, in start-up money to construct lawyer-like paneled offices and to hire a lawyer and a paralegal office administrator for each of the stores.

Zilberberg says his Law Centers will offer no-frills, cheap lawyering without sacrificing quality. The three lawyers he's hired have five years' experience each. He won't say how much he's paying them, but they'll get a piece of the action in addition to their salaries. He'll be saving a bundle, he figures, on low rent, no banks of secretaries, no massive libraries, no fancy artwork on the walls.

Zilberberg and his partners are confident the market for cut-rate legal services exists among working-class families who can't afford to pay either uptown-firm rates or even those charged by smaller firms.

The lawyer-entrepreneurs also are expecting some business from poor families who may be forced into the private market if the Reagan administration succeeds in wiping out or drastically reducing federally funded legal services.

Zilberberg and his partners are betting the family jewels they'll be able to tap that market, many of whose members would be more comfortable with a leper than a lawyer.

The first law centers will be in three prime Dart locations, Zilberberg says, stores with some 20,000 customers passing through each week. The stores are all 24-hour operations, and the lawyers will be there five days a week, one weekend day and will have a 24-hour answering service with lawyers on call. In addition, they will give 20 percent discounts for Dart's 4,000 employes.

Their biggest advantage will be advertising in the highly read Dart Sunday supplement. That's where discount coupons and price lists for divorces, wills, adoptions and other common legal needs will be advertised. Zilberberg says a substantial budget has been set aside for advertising: "Anything the market will bear and the bar (which monitors lawyer advertising) will allow."

The Dart operation is coming in ahead of Zayre Department Stores, which is thinking of opening law offices in it's Chicago and Miami stores early next year but has no plan yet for this area.

Dart is also moving into head-to-head competition with the local King of the Legal Clinics, Gary Gallo, who has opened six offices since starting in 1980.

Gallo, who spends thousands each week in media advertising and some direct-mail announcements, says he's not losing sleep over the prospect of competition, though the Dart operation will cut across his market in Annandale and Arlington.

The competition might actually help, he says, since it could get more people aware of an alternative to traditional law firms. On the other hand, he said, if too many clinics open, "maybe the market won't bear it." Gallo's prices and the prices Zilberberg says his firm will charge -- individual wills from $40, uncontested divorces from $195 -- are essentially the same. But there's always the chance for an old-fashioned price war now