Va. Code Ann. § 24.2-207

When any vacancy occurs in the representation of the Commonwealth of Virginia in the United States Senate, the Governor shall issue a writ of election to fill the vacancy for the remainder of the unexpired term. The election shall be held on the next succeeding November general election date or, if the vacancy occurs within 120 days prior to that date, on the second succeeding November general election date. The Governor may make a temporary appointment to fill the vacancy until the qualified voters fill the same by election.