The primary responsibility of the UN Security Council is to maintain international peace and security. This body is tasked with addressing threats to peace, responding to conflicts, and enabling peacekeeping initiatives. It plays a crucial role in the international system by making recommendations or taking action to prevent conflicts, enforce sanctions, and authorize the use of force when necessary.
In this context, the other choices, while important, do not fall under the UN Security Council's main functions. International trade agreements are generally handled by other entities such as the World Trade Organization. Global monetary cooperation typically involves institutions like the International Monetary Fund and the World Bank, focusing on economic stability and financial systems. Environmental sustainability is a focus of various UN agencies and initiatives but is not the core responsibility of the Security Council, which is more concentrated on issues that pose risks to peace rather than environmental concerns directly. Therefore, the emphasis on ensuring global stability and peace distinctly identifies the role of the UN Security Council.