To inhere is to be a permanent or essential part of something. A duty to do what's best for the American people inheres in the position of President of the United States.
Since the 16th century, inhere has been used for qualities that are intrinsic to something or someone. These day's it's an extremely formal way to talk about inherent characteristics: "To him, extreme competitiveness inheres in human nature, but I disagree." In legal writing, inhere is used for rights that are connected to owning property.