What does the Prime Minister do in relation to the UK's international representation?

The Prime Minister plays a crucial role in the international representation of the UK, as they lead the government and are responsible for shaping foreign policy. This position involves engaging with other countries, participating in international organizations, and addressing global issues such as trade, security, and diplomacy. The Prime Minister often meets with foreign leaders, attends international summits, and represents the UK in negotiations, all of which are fundamental responsibilities that ensure the country's interests and values are communicated and defended on the world stage. This comprehensive engagement underlines the Prime Minister's pivotal role in promoting the UK's position and influence internationally.

The other options do not encapsulate the full scope of the Prime Minister's responsibilities in a global context. While negotiating trade deals is an important aspect of international relations, it is only one part of a much broader role that includes leading the government and managing international affairs. Advising local governments falls outside the central focus of the Prime Minister’s international duties, and holding referendums is not a primary function of the role in terms of representing the UK internationally.