Governors are normally appointed for a fixed term as specified by governing instruments, usually three or four years.
Reappointment for one more term is permissible but not usually automatic, and the nominations committee should make a conscious recommendation about continuation in each case.
Reappointment for a third term is often discouraged and may even be forbidden. (The CUC Guide advises (paragraph 2.55) that continuous service beyond two terms of four years or three terms of three years is not desirable.) The exception is where a member has served for a few years, and then takes up office as chair of a committee or the chair of the governing body. In this case, an extension to the end of the natural run for the new role, if permissible under governing instruments, is obviously appropriate. Retiring members may wish to continue to support the institution and can be invited to adopt an ambassadorial role without being governors.
The rules for elected members will probably also specify how many times in succession they can stand, and sometimes there is a provision for a fallow period before re-election.