ALEXANDER'S ELECTION last week was a classic case of bipartism, ticket-splitting, Good Government voting. We use the capital letters to suggest that it wasn't merely a vote for better government. It was in that starchy civic tradition that demands tight administration, competence and rigorous law enforecement. The city's voters did a good job.

The city's reputation, it turns out, was very much on people's minds. They were fed up with the revelations about bingo payoffs, and the sniffering about massage parlors. To a good many Alexandriams, apparently, it didn't sound like the place where they liev - or would want to live. Their reaction was instructive. An unusual number of experienced and qulified people got into the race. Both parties had strong slates. For mayor, the voters chose Charles E. Beatley, a Democrat. For the council, they gave strong victories to three Democrats. It wasn't a flat rejection of the past, since two incumbents - one of each party - were reelected. But the new council promises to be stronger and more sharply focused than its predecessor.

What should it focus on? Beyond the matter of civic reputation, therehs the budget. Alexandria had resisted the impulse toward the kind of simplistic cutting by formula that, in the TRIM movements, was briefly popular in the Maryland suburbs last year. Alexandrians seem to recognize - again, in the Good Government tradition - that arbitrary curring is not good management. But it seems pretty clear that there's going to be a fierce hold-down on spending, including spending on scholls. Perhaps that's inevitable in view of the declining enrollments, but we urge caution. Educating children fron a very wide range of backgounds, as the alexandria school do, is onherently expensive. Fortunately, the new council includes Carlyle C. Ring, a former school-board president, who is in a position to do someting about some of the misunderstandings and abrasions between the schools and the people who must raise their funds.

The soaring value of real estate threatens serious damage to some of the city's neighborhoods, pushing out families who have lived there for years and drawing in speculative buyers. The first remedy, here and throughout Northern Virginia, is to find an alternative to the property tax for financing Metro. That takes state legislation, and so far Gov. John N. Dalton has shown neither interest nor concern. Perhaps there is an opportunity here for missionary work by the Republicans on the council. The need for legislation also points to the importance of the state legislators to be elected in Northern Virginia later this year.