The Justice Department has agreed that it will no longer refuse to hire a job applicant solely because he or she is living out of wedlock with a member of the opposite sex.

The agreement, in the form of a consent order, signed by U.S. District Court Chief Judge William B. Bryant, ends four years of litagation over the tricky issue of the government agency's right to deny employment because of an applicant's personal living arrangements.

John W. Karr, an attorney representing the female job applicant who brought the suit against the Justice Department in 1975, yesterday called the consent order a "significant victory" and said it marks the first time the Justice Department has been bound by a court order on the longbrewing issue.

Judith Scolnick, the Justice Department attorney assigned to defend the case, could not be reached for comment yesterday.

The consent order applies only to the central offices of the Justice Department and not to affiliated agencies such as the FBI, the Drug Enforcement Administration, the Bureau of Prisons, the U.S. Marshals Service, the Immigration and Naturalization Service and the Law Enforcement Assistance Administration.

The order grew out of a lawsuit brought in 1975 by Kathleen Bishop, then a student at Catholic University law school, who was turned down for a summer law clerk job after she acknowledged under questioning that she was living with a man out of wedlock.

As the case dragged on it court, Bishop completed law school and obtained employment elsewhere. The Justice Department denied having a policy of rejecting applicants such as Bishop, and contended, among other things, that the case was moot since the job Bishop originally applied for was for law students only.

Judge Bryant refused to dismiss the case, however. Lawyers on both sides continued to wrangle over technical issues, and the litigation never reached the central issue of the Justice Department's reason for denying Bishop employment. Then last week, the department agreed to the consent order signed Thursday by Bryant.

The brief but carefully worded consent order says that the Justice Department agreed it "shall not find a person unsuitable for employment solely because that person resides with and/or engages in sexual intercourse with an unrelated member (or members) of the opposite sex."

Also, the department agreed it will no longer refuse to hire an applicant "solely based on unsubstantiated conclusions concerning possible embarrassment to the Department of Justice."

The consent order adds, however, that the department may find a job applicant unsuitable if his or her residence or sexual intercourse with another person "affects job fitness."

While the order does not specify what might adversely affect "job fitness" it suggests that such a judgement must be based on specific evidence, rather than "unsubstantiated conclusions."

The much-debated issue of private living arrangements, or "extramarital cohabitation," as it is called in formal court papers, has been litigated in various courts and administrative offices in recent years by job applicants and employes at numerous agencies, but the cases have rarely resulted in a definitive ruling as in the Bishop case.

FBI employes have fought being fired or transferred both for living out of wedlock and for being homosexuals, but they have had little luck in the courts.

Last July, however, FBI director William H.Webster said the bureau would no longer dictate the private life styles of its employes.

"We're trying to stay out of people's private lives" he said, "unless their conduct -- and the emphasis is always on conduct, not personal beliefs -- impacts upon the effectiveness of that individual and the bureau," he said.

Bishop is employed today in an administrative job at the Department of Housing and Urban Development.

One of those who are waiting is Jack Shaw, a neighbor of Kennedy and co-worker at AT&T who drives a gas-guzzling Lincoln in a carpool two days a week.

"I'd just as soon stay and pay my present mortgage rate of 7 1/2 percent as to have it doubled in Virginia," he says. "With $600 or $700 mortgage payments, I probably couldn't even go out and eat at McDonald's."