Although FAIR Research Data Principles are targeted at and implemented by different communities, research disciplines, and research stakeholders (data stewards, curators, etc.), there is no conclusive way to determine the level of FAIRness intended or required to make research artefacts (including, but not limited to, research data) Findable, Accessible, Interoperable, and Reusable. The FAIR Principles cover all types of digital objects, metadata, and infrastructures. However, they focus their narrative on data features that support their reusability. FAIR defines principles, not standards, and therefore they do not propose a mechanism to achieve the behaviours they describe in an attempt to be technology/implementation neutral. A range of FAIR assessment metrics and tools have been designed that measure FAIRness. Unfortunately, the same digital objects assessed by different tools often exhibit widely different outcomes because of these independent interpretations of FAIR. This results in confusion among the publishers, the funders, and the users of digital research objects. Moreover, in the absence of a standard and transparent definition of what constitutes FAIR behaviours, there is a temptation to define existing approaches as being FAIR-compliant rather than having FAIR define the expected behaviours. This whitepaper identifies three high-level stakeholder categories -FAIR decision and policymakers, FAIR custodians, and FAIR practitioners - and provides examples outlining specific stakeholders' (hypothetical but anticipated) needs. It also examines possible models for governance based on the existing peer efforts, standardisation bodies, and other ways to acknowledge specifications and potential benefits. This whitepaper can serve as a starting point to foster an open discussion around FAIRness governance and the mechanism(s) that could be used to implement it, to be trusted, broadly representative, appropriately scoped, and sustainable. We invite engagement in this conversation in an open Google Group fair-assessment-governance@googlegroups.com