A circle is a special kind of role from the supercircle's point of view. Therefore, to change the purpose of a circle, you will need to open a Governance Meeting for the supercircle. From there, you can edit the role (that is a circle) and modify the purpose. By modifying this role's purpose, the circle's purpose will be modified also.
In the screenshot below, "House" is a subcircle of the "People & Partnership" circle. To change the purpose of the House circle, a governance meeting was opened for People and Partnership. Then, by selecting "Add/Edit Role" and choosing "House", the purpose of the circle can be modified. Note the "Remove this circle" option at the bottom of the proposal, indicating that this role is a circle.
Related: How do I change the purpose of my organization?