Elected in October for a 12 month term.
According to the Constitution:
Article III Elections and Vacancies in the Senate. Section 3
The October Vacancy Election shall take place on the second Tuesday in October for the purpose of filling any vacancies that are created between the time of the ratification of the May election results and October 1, as declared by the Speaker. One of the undeclared Senators and the Maverick Hall Senator shall also be elected in the October Vacancy Election and shall have their term expire the day of ratification of the following year's October Election results.