Final answer:
The correct answer is City Manager, as they handle administrative functions in a council-manager system which typically includes overseeing employment matters.
Step-by-step explanation:
The question pertains to the requirements for fire department personnel who desire to seek external employment for profit or gain. According to the context provided, individuals who wish to engage in outside employment must obtain permission. While the specifics can vary by department or municipality, in a council-manager system of government, the city manager is typically appointed by the city council to handle administrative functions, which may likely include granting permission for such employment.
Therefore, the correct answer to the question is: Members desiring employment outside the fire department for profit or gain are required to fill out an application for permission from the City Manager.