Legally, employees can no longer be compelled to retire simply on the basis of age (see
http://www.bbc.co.uk/news/business-15127835). However, employers have various options. An employer can compulsorily retire an employee on objective grounds, in effect on the basis that they are no longer able to carry out the work to a satisfactory standard. Or an employer can simply dismiss an employee along with an offer of compensation and (usually) a compromise agreement that binds both parties to confidentiality and it being a final settlement. Or the employer can simply negotiate with the employee, possibly offering a golden handshake as an incentive.
My feeling is that the contract of employment should not be secret. Commonly it is available to all and sundry when a vacancy occurs - often the contract is part of a bundle of documents available to anyone who expresses an interest in applying - perhaps available for download by anyone from a web site. If it is not made public, it would certainly be my view that the councillors' common law right of access to council documents would cover the clerk's contract. A contract of employment should be reviewed periodically, not so much by reference to the age of the employee, but because law and best practice change over time. For general advice on employment contracts, see
https://www.gov.uk/employment-contracts-and-conditions/overview.
A clerk cannot be self employed and a council that has a paid clerk must operate PAYE. This is plainly stated by HMRC at
https://www.gov.uk/hmrc-internal-manuals/employment-income-manual/eim67300 and has been the case for some years now.