Alexandria School Board Chairman Alison M. May announced last night she has decided against seeking appointment to a fourth three-year term on the city school board.

May, 49, who has been chairman for the last two of her nine years on the board, said before last night's meeting that "it is time for new blood." She added that a desire to spend more time at her stockbroker's job was another factor in her decision.

A politically active Democrat who lost a race for the City Council in 1970, May said she "has no plans at this time" to seek another public office.

She said school desegregation moves in the early 1970s and selection of a school superintendent were the most important issues that faced the board during her years on it. A desegregation plan was implemented on a gradual basis beginning in 1970. John L. Briston, the outgoing school superintendent, was hired in 1970. May said the process of finding a successor to Briston is also a demanding task.

There are nine members on the school board; three are appointed by the City Councl each year. Board member Michael Mulroney has announced he is not seeking a third term. Member Lou Cook has said she is seeking a second term.

Board members receive $125 a month and serve for three year terms.