Fairfax County School Superintendent Robert R. Spillane said last night he will not rehire former Redskins running back Clarence Harmon, who resigned as a Langley High School aide and volunteer coach after it was disclosed that officials did not know of his involvement in a drug case in Texas when they hired him.

Spillane said the Texas case played a role in the decision by him and the School Board not to take Harmon back, but indicated that other factors, which he would not disclose, also were involved.

"We've accepted his resignation," Spillane said after the board met for an hour in closed session to discuss the Harmon case and other matters. "His resignation stays. He won't be coming back to this system."

Spillane said, "from my perspective, his best interests and the schools' best interests are mutually served by him not returning."

Harmon had no comment last night.

Harmon, who was hired this fall, resigned Sept. 19 after school officials learned that he had pleaded guilty to possession of a controlled subject in Texas two years ago. On Sept. 24 he asked for his job back after receiving a flood of encouragement from supporters.

In the widely publicized Texas case, he was fined $5,000 and placed on probation for two to 10 years. Under Texas law, he is not considered to have a criminal record.

In other action, the School Board voted to pay $200,000 to speed construction of Union Mill and Salisbury elementary schools in the Centreville area. They are to be completed by next Aug. 15 rather than Dec. 1, 1986, as scheduled.

That means the schools would open for the beginning of the 1986-87 school year, rather than in January 1987.

At the board's last meeting, on Sept. 26, Kohann H. Whitney, the Centreville representative, said the new schools would significantly alleviate overcrowding that has forced educators to contract for temporary classroom buildings.

The board also is studying how to speed construction of Sully Elementary School in the Franklin Farms section, which has not yet been put out to bid. It is to open in September 1987.