Transportation Secretary Brock Adams, using money left over from his earlier congressional campaigns, has established a $50,800 trust fund to be used for campaign costs should he run for public office after leaving the Cabinet.

Adams established the trust fund last spring after clearing it with White House lawyers. But White House officials never saw a copy of the actual trust agreement, which, it turns out, does not precisely meet the conditions laid down by the White House in approving the fund.

Michael H. Cardozo, an associate White House counsel, said yesterday that the trustees probably will be asked to change the language in the agreement to require that if Adams does not use the money in a political campaign, the funds go to a charity.

Bob olland, a Transportation Department spokesman, quoted Adams as saying he is willing to make whatever changes are necessary.

There is nothing illegal about the trust fund. Under federal law, Adams could legally use the $50,800 for personal expenses so long as long as he reported it as income.

Adams is known to be interested in running for the Senate from his home state of Washington if Sen. Warren G. Magnuson (D) does not seek re-election in 1980.

According to Cardozo, when the White House approved establishment of the trust fund last April it laid down two conditions: that the money, and any interest from it, be used to finance a future Adams political campaign, or that the funds be donated to charity.

However, the trust agreement, a copy of which an Adams aide had at the Department of Transportation but which the White House lawyers nevered saw says that if Adams has not run for public office by 1985 the trustees are to meet and disperse the funds in a manner that "best respects the desires of the contributors of the funds."

It makes no mention of donating the funds to charity although Holland said that has always been the trustees' intention.

Under no circumstances, Holland and Cardozo said, would Adams accept any of the money for his personal use.