The Supreme Court begins its 1985-86 session.

Lord Carrington, the NATO secretary-general, holds an 11:15 a.m. briefing at the State Department on his meetings with U.S. officials, including President Reagan.

The President's Commission on Organized Crime holds a symposium on drug interdiction, beginning at 9 a.m. at 1425 K St. NW, Suite 700.

The House Democratic Caucus holds a 1 p.m. news conference to unveil a program to try to reach young voters.

The National Organization for Women plans a motorcade and rally to protest what it calls "the ideological court-packing" of the Reagan administration. The motorcade begins at 10:30 a.m. on Constitution Avenue across from the Ellipse and is followed by the rally at 11:45 at the Capitol. TUESDAY

The president meets with Singapore Prime Minister Lee Kuan Yew and hosts a state dinner for him. WEDNESDAY

The Cato Institute holds a policy forum on "The Need for Fundamental Tax Reform," 4 p.m. to 5:30 p.m. at the institute, 224 Second St. SE. Phone 546-0200.

Trade policy and international competitiveness are the focus of an all-day symposium featuring Sen. Bill Bradley (D-N.J.), Sen. Albert Gore Jr. (D-Tenn.) and Rep. Timothy E. Wirth (D-Colo.), in the Senate Caucus Room of the Russell Building. Call Tim Holder at 863-8002 for details. THURSDAY

Reagan flies to Chicago to lobby for his tax-revision package.

Increasing quantities of carbon dioxide and what effect they will have on the Earth's climate will be the subject of an 8 p.m. lecture at the National Academy of Sciences, 2101 C St. NW. Call 334-2000. Former EPA administrator William D. Ruckelshaus speaks at a briefing on the U.N. World Commission on Environment and Development, 10 a.m. in Room EF-100 of the Capitol. The event is sponsored by the Environmental and Energy Study Conference. Call Jon Clark at 863-1900 for details.