In this paper, the relation between the FAIR (Findable, Accessible, Interoperable, Reusable) ontologies and accountability and transparency of ontology-based AI systems is analysed. Also, governance-related gaps in ontology quality evaluation metrics were identified by examining their relation with FAIR principles and FAcct (Fairness, Accountability, Transparency) governance aspects. A simple SKOS vocabulary, titled "Hospital Adverse Incidents Classification Scheme" (HAICS) has been used as a use case for this study. Theoretically, we found that there is a straight relation between FAIR principles and FAccT AI, which means that FAIR ontologies enhance transparency and accountability in ontology-based AI systems. We suggest that "FAIRness" should be assessed as one of the ontology quality evaluation aspects.