A company’s directory services server is located on premises.

In CompTIA A+ Core 1 (220-1201) cloud concepts, the key differentiator between cloud deployment models is where the service is hosted and who owns/uses the underlying infrastructure. If a company’s directory services server (for example, a domain controller providing authentication/authorization and centralized identity management) is located on premises, that points to infrastructure that is owned and operated by the organization for its own internal use. This aligns best with a private cloud model, which is defined as cloud resources dedicated to a single organization and can be implemented on-premises (internally hosted) or in a dedicated off-site environment.

It is not a public cloud because public cloud services are hosted by a third-party provider and shared across multiple customers. It is not hybrid cloud because hybrid requires a mix of on-prem resources and public cloud resources working together (the question only specifies on-prem). It is not community cloud because that involves shared infrastructure among multiple organizations with common needs.