Final answer:
A nurse can obtain licensure in a second state through a process known as licensure by endorsement, which allows them to be granted licensure based on their existing credentials without retaking the examination.
Step-by-step explanation:
When a nurse holds a license in one state and seeks to practice in another state that is not a part of the nurse licensure compact agreement, they can obtain licensure in the second state by a process known as licensure by endorsement. This involves the nurse being granted licensure upon payment of a fee without needing to retake the licensure examination. Licensure by endorsement allows for the recognition of the nurse's qualifications and licensure from the original state, under the assumption that their credentials meet or exceed the requirements of the new state.
Other methods mentioned, such as through mandatory continuing education, being grandfathered, or through sunset legislation, are not the correct processes for a nurse to achieve licensure in another state under the described circumstances.