Выражение встречается в следующем контексте:......he commanded a battalion in Saudi Arabia that "cleared out the theater" of all remaining U.S. materiels.

Заранее спасибо

в данном контексте означает "эвакуировать".

употребляется также и в ироничном значении "разогнать всех" (Например так могут сказать про плохого актера: By the end of the show he cleared out the theatre.)

Most everyone agrees that a precipitous American withdrawal from Iraq would be disastrous. Fewer people realize it may be impossible. In the past four years, the U.S. military has shipped to the region more than 9 million tons of equipment—from tanks and bulldozers to toilets and silverware. If you were to load all that gear on tractor-trailers and line them up end to end, the convoy would extend from San Francisco to Miami.

"It's mind-boggling, the size of all this," says Maj. Gen. Charles W. Fletcher Jr., who is director of operations at the U.S. Transportation Command and was in charge of logistics at the start of the war. Fletcher knows something about pullouts. After the 1991 war in Iraq, he commanded a battalion in Saudi Arabia that "cleared out the theater" of all remaining U.S. matériel. "We let all the soldiers fly home minus myself and a couple of thousand others," he says. "It took us about eight months to get all the equipment back."

By Dan Ephron
Newsweek
April 23, 2007

Здесь идет прямая речь внутри авторской речи, но в принципе можно сказать и обеспечил транспортировку армейского имущества с театра военных действий после того, как "представление" закончилось....