Va. Code § 15.2-1424
Vacancies in the office of board of supervisors or of council or an elected chairman or mayor, for whatever reason, shall be filled as provided for in Title 24.2. A member of the board or council may be elected or appointed to fill a vacancy in the office of chairman or mayor.
The person appointed or elected to fill the vacancy shall possess the same legal qualifications for the office as did the person whose position he is filling.
In the event of a vacancy in the office of chairman or mayor, the duties of the office of chairman or mayor shall be performed by the vice-chairman or vice-mayor until a chairman or mayor is appointed or elected and qualifies.
Vacancies in the office of vice-chairman or vice-mayor shall be filled by appointment by the remaining members of the appropriate governing body from its membership.
Va. Code § 15.2-1424