Former Virginia attorney general Andrew P. Miller, now a Washington lawyer, added his name yesterday to the list of candidates seeking to fill a newly vacant seat on the Virginia Supreme Court.

Miller, who in the last two years lost bids to become governor and U.S. senator, said he would allow his name to be considered by the state legislature, which will fill the post after it convenes Jan. 9.

Justice Alex M. Harman Jr. of Pulaski County in Southwest Virginia, is retiring from the court at the end of the year because of ill health. The Richmond court has the reputation of being one of the most conservative -- critics say reactionary -- judicial bodies in the nation.

In addition to Miller, who is a partner in the Washington law firm of Dickstein, Shapiro and Morin, leading contenders for the $50,000 a-Year post are said to include Circuit Court Judge W. Carrington Thompson of Chatham, a former legislator, former Del. Carrington Williams of Fairfax County and former House of Delegates Appropriations Committee Chairman Edward E. Lane of Richmond.

Because he hails from Southwest Virginia and has strong ties to the legislature, Thompson is considered a front-runner. Miller, who practiced law in the Southwest town of Abingdon before he was first elected attorney general in 1969, may also take a territorial claim and also has numerous political allies in the General Assembly.