I believe it refers to the entire monastic sangha. The term is found in a couple of places in the Theravada Vinaya:
“Well now, do you, householder, establish these sixty dwelling-places for (the use of) the Order of the four quarters, present and to come.”
“Very well, Lord,” and the (great) merchant of Rājagaha, having answered the Lord in assent, had those sixty dwelling-places established for (the use of) the Order of the four quarters, present and to come.
Now at that time a certain monk who had many goods, many requisites, came to pass away. They told this matter to the Lord. He said: “Monks, the Order is the owner of the bowl and robes of a monk who has passed away. But truly those who tend the sick are of great service. I allow you, monks, to give through the Order the three robes and the bowl to those who tended the sick; to distribute through the Order that is present whatever few goods, few requisites are there; but whatever many goods, many requisites are there, these are for the Order of the four quarters—those who have come in, those who have not come in—they are not to be disposed of, not to be divided up.”
From Sujato’s Blog:
The main paradigm is that of a monastery given to the Sangha of the Four Quarters. This means all Buddhist monastics, past and future.
From VINAYA: Ownership and Administration of Monasteries, by Ajahn Brahm:
In the time of the Buddha, when a lay Buddhist offered lands of buildings, or money for such things, to establish a monastery, they would dedicate it to The Sangha of the Four Quarters Present and Yet to Come . The Sangha of the four quarters present and yet to come means ALL properly ordained monks and nuns.