Most institutions will have provisions relating to the appointment of governors in their statutory documents (usually the charter and statutes; memorandum and articles of government or ordinances or regulations).
These are likely to be similar to the requirements of the Companies Act 2006, relating to the appointment of company directors. The restrictions on the appointment of directors are that they must not have been disqualified from acting as a director; they must not be an undischarged bankrupt and must not be under the age of 16.
There are also legal restrictions on who may be a charity trustee, deriving from the Charities Act 1993. This prohibits the following from serving as a charity trustee:
In addition, no-one under the age of 18 may be a trustee of a charitable trust.
Once appointed as a governor most institutions have provisions concerning the termination of the appointment. These will normally cover the circumstances above, and may also enable the governing body to terminate the appointment in the event of significant non-attendance; mental or physical infirmity; or bankruptcy.
Many institutions now have codes of conduct for governors which cover these matters as part of the expectations of governors.