Joel W. (Jay) Solomon, the new chief of the General Services Administration, which builds and rents office space for the federal government, is a large stockholder in a GSA contractor.

Solomon, 55, a shopping center developer from Chattanooga, owns about 300,000 shares of stock worth more than $900,000 in the giant Arlen Realty and Development Corp.

The firm and its subsidiary, Arlen Shopping Centers Co., lease space to the GSA in 13-buildings across the country, Solomon told the Senate last month.

He said GSA pays Arlen about $1 million a year for the premises, which include space used for five Social Security offices and an Internal Revenue Service branch.

Before his Senate confirmation last Friday, Solomon agreed to resign as an officer of the New York-based development corporation and pledged that he would not take part in any more than $900,000 in the giant Arlen.

In a letter to Sen. Abraham Ribicoff (D-Conn.), chairman of the Governmantal Affairs Committee, which unanimously recommended Solomon's confirmation, the new administrator agreed to turn over any GSA matter that involves Arlen to his deputy, Robert Griffin.

He also agreed to donate to charity any profits he might receive if Arlen wins a claim against the GSA for space leased to the Labor Department in Dallas. GSA is claiming $52,200 in damages because Arlen didn't deliver the space on time, and Arlen is claiming $150,192 for extras and additional rent because the department got more space than it originally sought.

But Solomon wrote another committee member, Sen. Charles H. Percy (R-Ill.), last week that he could not comply with Percy's request that he donate to charity Arlen-related profits from GSA. He said such figures are hard to determine and such a donation "could constitute an unfair financial burden."

Percy based the request on an "appearance of a potential conflict of interest." Ribicoff, however, said before the Senate vote that everything possible was done to "insulate Solomon from Arlen Realty."

Before his confirmation hearing Solomon wrote the committee that he had been in real estate development since 1961 and that in 1970 his firm, Independent Enterprises Inc., was merged into Arlen Shopping Centers Inc. The next year, he said, the shopping center company merged with Spartan Industries Inc. and became Arlen Realty and Development Corp.

"I came into Arlen on the basis of $12.50 stock price," he told the committee, but he added that now "the stock is very low." Last Friday Arlen closed at $3.125 a share.

Solomon said he was considering "selling some of the stock as I go along . . . after I get settled down in office because, as you know, there is a great financial loss coming into the government."

As head of the GSA, Solomon will make $52,000 a year.

Last year he gave $2,000 to the senatorial campaign of James Sasser (D-Tenn.), who heads the Governmental Affairs subcommittee that deals with the GSA. Solomon's wife Rosalind donated $1,500 and son Joel Jr. donated $132 to Sasser's campaign. Daughter Linda, a student at Northwestern University in Illinois, worked three months, at $750 a month, as a field organizer for Sasser.

Solomon and his wife also gave $1,000 each to the Carter presidential campaign and help raised additional funds for Carter.

Sasser's administrative assistant, Jerry Grant, said, "Jay Solomon is eminently qualified to be the administrator of GSA. He didn't seek the job . . . This is the idea of Hamilton Jordan," the President's political adviser.