Arlington County, once renowned for its liberal public school system, hired a fiscal conservative yesterday as its new school superintendent, the latest mark of a countywide trend toward more conservative government.

Charles E. Nunley, now head of the Lorain, Ohio, schools, was named to the $56,000-a-year Arlington job to oversee a 15,146-pupil school system beset by declining enrollment, a growing minority and immigrant population and soaring costs.

Nunley, who will assume his duties July 1, succeeds former superintendent Larry Cuban, who announced his resignation in March under pressure from county conservatives.

Nunley was the choice of four of Arlington's five school board members, who winnowed its list from nearly 60 applicants to eight and then to three finalists, school officials said. Board member Ann C. Broder, a longtime leader of the board's liberal faction, was not present when Nunley was selected.

A veteran of 28 years in public education, Nunley said yesterday he expects his major tasks in Arlington will be "resolving the fiscal situation, the declining enrollment and the communications issues that some [teacher representatives] brought up on my visit there."

Arlington teachers generally feel they have had no say in policy decisions Nunley said he was told.

Arlington school board chairman O.U. Johansen said Nunley was selected primarily because of his capacity for financial mamagement. "He came to Lorain at a time when their school system was in serious fiscal difficulties and put them in the black . . .," Johansen said.

Arlington schools now have a $1.5 million deficit and the County Board has tentatively agreed to increase the system's budget by 11 percent next year -- well under the amount sought by county teachers and te school board.

Johansen cited school closings, secondary school reorganization, and employe layoffs as serious problems with which Nunley is also going to have to deal. "He's had experience in these areas," Johansen said.

Nunley, who has a doctorate in school administration, endured two teachers' strikes in Lorain, one of which was precipitated by teacher layoffs for budget reasons.

As a result, Nunley's relations with teachers were strained and they sought his firing, said Lorain school board president Kenneth Koscho, who voted with the board majority against rehiring him in July. But, Koscho added, "I think highly of him and think he is a most able administrator."

Apparently criticizing Cuban, whose seven-year tenure was marked by clashes with Johansen and the County Board over money matters, Johansen said, "We would like to see a superintendent begin working and administering a school system in such a way as the stated goals of the school system can be advanced."

Nunley, Johansen said, is " a pragmatist who is going to attempt to run the school system in accordance with the prevailing citizen sentiment and feelings." Recently much of that sentiment has embraced the conservative "back-to-basics" movement.

Nunley, who has been superintendent since 1975 in Lorain, an industrial city of 80,000 people 30 miles west of Cleveland, said yesterday he dislikes "back-to-basics" labels. "Yes, I'm a conservative fiscally, but I'm a moderate on instruction," he said.

"I'm a strong advocate of basics. Some things you need to be conservative with, such as basic skills; others, you need to be more liberal . . . But when some people talk about back-to-basics they're only talking about reading, writing and arithmetic and they neglect the humanities, which I think are important.

"We've gotten too generous in straying from the most important task, which is the mastery of basic skills, too generous in creating alternatives, electives, options. We need to evaluate those very carefully."

Nunley, who learned he was a finalist while in Chile on a cultural exchange visit, is also the architect of what he describes as "a plan to reduce racial isolation" in Lorain in 1978 by redistribution minority enrollments while avoiding busing.