Final answer:
An agreement to waive prior rights in favor of another is known as subordination. The social contract is the philosophical concept where citizens consent to governance in exchange for the protection of their natural rights.
Step-by-step explanation:
An agreement to waive prior rights in favor of another is called subordination. This term is used in law, particularly in real estate and finance, where a party with a claim on assets or interests agrees to allow their claim to be ranked below the claim of another.
However, to clarify the concept presented in the second part of your question: the agreement that citizens will consent to be governed so long as government protects their natural rights is called the social contract. This idea is a foundational theory in modern political philosophy and is associated with enlightenment thinkers like Thomas Hobbes, John Locke, and Jean-Jacques Rousseau.