One of the fresh new faces of 1991 belongs to Sharon Pratt Dixon, inaugurated mayor of Washington, D.C., last week.

Known for a smile as broad as her landslide victory at the polls was wide, Mrs. Dixon is promising a badly needed rejuvenation for the nation's capital.

It's easier to promise than deliver, given the magnitude of Washington's woes: another record murder rate last year, a $300 million budget deficit and the racial polarization heightened by the sensational and divisive cocaine trial of her three-term predecessor, Marion Barry.

Dixon, a former utility company executive and former treasurer of the Democratic National Committee, has gutsy plans to slash the city payroll and streamline operations.

She talks about efficiency and service. She says, "What the people of Washington want most is an honest deal."

She's right about that. The rest of the country will be grateful, too, if she succeeds in restoring the capital's self-respect.