How long to keep documents
There aren't any specific rules about how long to store governing board documents for, unless they contain personal data (more information on this below).
The DfE guidance on data protection in schools suggests that schools should check each year what data they hold and decide if they still need to keep it - this could also be a good idea for your board. They also suggest creating a data retention schedule, which could help you keep track of what you are storing and when to get rid of it.
If your documents contain personal data
It's a legal requirement under the UK General Data Protection Regulation (GDPR) to store personal data only for as long as is necessary for the reasons it was collected.