Yes. Parents are eligible to be the chair or vice-chair of governors at both maintained schools and academies. The only exception is that they cannot also work for the school or academy, because school employees are not allowed to chair governing bodies.
This is explained in the law for maintained schools. It is also in model articles of association for academies (June 2021).
“A governor who is employed at the school as a teacher or as any other member of the school’s staff is not eligible to be chair or vice-chair of the governing body of that school.”
Roles, Procedures and Allowances (England) Regulations 2013
“The trustees shall each school year elect a chair and a vice-chair from among their number. A trustee who is employed by the academy trust shall not be eligible for election as chair or vice-chair.”
Model Articles of Association (June 2021)
In a maintained school parents can join the governing body either in the specific “parent governor” category or as a co-opted governor, local authority governor or foundation governor.
Parents can also be partnership governors in a maintained school as long as they do not currently have a child who is a registered pupil at that specific school. Separate articles provide more detail on who can be a parent governor and general governor types and eligibility.
Note that if you wish to join the board under the specific “parent governor” category there are two restrictions for maintained schools – you cannot work for the school for more than 500 hours per year and you cannot be an elected member of the local authority. If you work for the school for 500 hours or less per year you can be a parent governor but not the chair or vice-chair.
Academies have parent trustee (and sometimes parent local governor) roles. They often have co-opted roles as well which are open to any member of the public.