Alexandria School Board members said they were surprised and a somewhat disappointed last week when the City Council rejected incumbent board member J. Harvey Harrison's bid for reappointment.

Surprised because Harrison was seen as a hard-working, dedicated board member.

And disappointed because the vote was along strict party lines, with the four Democrats voting against the reappointment and the three Republicans voting for it.

"I don't like to see board appointments depend on political affiliation," said school board member William Euille. "The school board should be nonpartisan and concerned solely with the good of the school system."

All school board members, however, were quick to point out that council and school board relations have been very amicable.

"We've achieved a very good working relationship with the council . . . ," Euille said. "We get along well together."

The council filled three posts on the nine-member school board. The new members are Lynwood Campbell Jr., Sandra Lindsay and Timothy Elliott. They will fill the posts vacated by Harrison, board Chairman Shirley N. Tyler and Vice Chairman Claudia Waller. All board members are appointed to three-year terms. Harrison was the only one of three, whose terms expired today, who sought reappointment.

The morning after the appointments, Harrison said he was stunned by the vote.

"I was disappointed," he said. "I think we do need a good, cost-effective education system. I was happy to give my expertise."

However, some council members and school board colleagues said Harrison, an outspoken Republican, may have been partly responsible for the political vote that blocked his reappointment.

"He did a good job, but he stood out politically," said veteran school board member Judith Feaver, who added that Harrison will be sorely missed. "We need him. . . . We could use his expertise."

Harrison is not out of the picture yet. Last week, two council members--Democrats Donald V. Casey and James P. Moran Jr.--indicated they would vote to appoint Harrison to the next board vacancy. Since board member James Skidmore has announced he has been transferred and is moving from Alexandria next month, Harrison could be back on the board by the end of the summer.

Despite complaints about the vote, at least one council member, Republican Carlyle C. Ring Jr., rejected the idea that the decision was based only on party politics. "Sometimes you have to reject first-rate people in order to vote for your first choice," said Ring, who noted that he doesn't even know the party affiliations of the three appointees. "You pick the best people. And if you have two good people you take party affiliation into account."

Ring added, however, "I was very disappointed Harrison was not reappointed. He was an incumbent who has done a good job."

Two of the three new members--Campbell and Lindsay--have been involved with city schools for several years.

Campbell, who has served on the school budget advisory committee, said he is particularly interested in budget matters.

"We have a tight budget and there is no room to tighten it more," he said. "You have to look at all the cuts in terms of programs now. In most cases it is better to cut subjects than classes."

Campbell has been criticized by some for sending his only child to a private school, but he said his 11-year-old daughter made her own decision to attend St. Mary's Elementary School, a parochial school in Alexandria. "The council was very interested in that, but I told them she is a very independent little lady," said Campbell, who also attended St. Mary's.

Lindsay, who works for a local construction firm, is a past president of the Alexandria PTA Council. Her son graduated this month from T.C. Williams High School and her daughter will be a junior there this fall.

Lindsay said she is interested in the impact a tighter budget will have on schools. "There is the belief that some classes and programs are non-essential because there aren't many students involved in them," she said, "but you can't base decisions on student enrollment."

Elliott, the third new member, is an Interior Department attorney with two children in Alexandria schools. Elliott said he would like to see school administrators, teachers and staff evaluated more thoroughly.

The six incumbent school board members say they are pleased with the council choices.

"These are just the people we need on the board," said Feaver. "They will help make it a strong board."