With spectrum resources becoming congested and the emergence of sensing-enabled wireless applications, conventional resource allocation methods need a revamp to support communications-only, sensing-only, and integrated sensing and communication (ISaC) services together. In this letter, we propose two joint spectrum partitioning (SP) and power allocation (PA) schemes to maximize the aggregate sensing and communication performance as well as corresponding energy efficiency (EE) of a semi-ISaC system that supports all three services in a unified manner. The proposed framework captures the priority of the distinct services, impact of target clutters, power budget and bandwidth constraints, and sensing and communication quality-of-service (QoS) requirements. We reveal that the former problem is jointly convex and the latter is a non-convex problem that can be solved optimally by exploiting fractional and parametric programming techniques. Numerical results verify the effectiveness of proposed schemes and extract novel insights related to the impact of the priority and QoS requirements of distinct services on the performance of semi-ISaC networks.