The responsibility of MR are well explained in the related clause of ISO 9001 standard.
Clearly you should tailor this responsibility, also enriching your role.
WHat are the expectations of the top management towards your role?.
This could be a good starting point together the reference of the standard.
For example, the first practical things I got in mind are the planning of the internal audits and results reporting, management of corrective and preventive action, support for Quality Documentation ( procedure, manual , etc.), fostering Quality culture into the organization , interface with Registrar , support to the organization in managing Customer audit, support the organization for SUpplier audit and so on.
Hope this helps